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- Ruth–Aaron_pair abstract "In mathematics, a Ruth–Aaron pair consists of two consecutive integers (e.g. 714 and 715) for which the sums of the prime factors of each integer are equal:714 = 2 × 3 × 7 × 17715 = 5 × 11 × 13and 2 + 3 + 7 + 17 = 5 + 11 + 13 = 29If only distinct prime factors are counted, the first few Ruth–Aaron pairs are:(5, 6), (24, 25), (49, 50), (77, 78), (104, 105), (153, 154), (369, 370), (492, 493), (714, 715), (1682, 1683), (2107, 2108)(The lesser of each pair is listed in (sequence A006145 in OEIS)).Counting repeated prime factors (e.g. 8 = 2×2×2 and 9 = 3×3 with 2+2+2 = 3+3), the first few Ruth–Aaron pairs are:(5, 6), (8, 9), (15, 16), (77, 78), (125, 126), (714, 715), (948, 949), (1330, 1331)(The lesser of each pair is listed in OEIS A039752).The intersection of the two lists begins:(5, 6), (77, 78), (714, 715), (5405, 5406)(The lesser of each pair is listed in OEIS A039753).Any Ruth–Aaron pair of square-free integers belongs to both lists with the same sum of prime factors. The intersection also contains pairs that are not square-free, for example (7129199, 7129200) = (7×112×19×443, 24×3×52×13×457). Here 7+11+19+443 = 2+3+5+13+457 = 480, and also 7+11+11+19+443 = 2+2+2+2+3+5+5+13+457 = 491.The name was given by Carl Pomerance for Babe Ruth and Hank Aaron, as Ruth's career regular-season home run total was 714, a record which Aaron eclipsed on April 8, 1974, when he hit his 715th career home run. Pomerance was a mathematician at the University of Georgia at the time Aaron (a member of the nearby Atlanta Braves) broke Ruth's record, and the student of one of Pomerance's colleagues noticed that the sums of the prime factors of 714 and 715 were equal.".
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- Ruth–Aaron_pair wikiPageExternalLink puzz_358.htm.
- Ruth–Aaron_pair wikiPageID "4886430".
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- Ruth–Aaron_pair wikiPageOutDegree "33".
- Ruth–Aaron_pair wikiPageRevisionID "660690895".
- Ruth–Aaron_pair wikiPageWikiLink 104_(number).
- Ruth–Aaron_pair wikiPageWikiLink 105_(number).
- Ruth–Aaron_pair wikiPageWikiLink 125_(number).
- Ruth–Aaron_pair wikiPageWikiLink 126_(number).
- Ruth–Aaron_pair wikiPageWikiLink 153_(number).
- Ruth–Aaron_pair wikiPageWikiLink 154_(number).
- Ruth–Aaron_pair wikiPageWikiLink 15_(number).
- Ruth–Aaron_pair wikiPageWikiLink 16_(number).
- Ruth–Aaron_pair wikiPageWikiLink 24_(number).
- Ruth–Aaron_pair wikiPageWikiLink 25_(number).
- Ruth–Aaron_pair wikiPageWikiLink 49_(number).
- Ruth–Aaron_pair wikiPageWikiLink 50_(number).
- Ruth–Aaron_pair wikiPageWikiLink 5_(number).
- Ruth–Aaron_pair wikiPageWikiLink 6_(number).
- Ruth–Aaron_pair wikiPageWikiLink 77_(number).
- Ruth–Aaron_pair wikiPageWikiLink 78_(number).
- Ruth–Aaron_pair wikiPageWikiLink 8_(number).
- Ruth–Aaron_pair wikiPageWikiLink 9_(number).
- Ruth–Aaron_pair wikiPageWikiLink Atlanta_Braves.
- Ruth–Aaron_pair wikiPageWikiLink Babe_Ruth.
- Ruth–Aaron_pair wikiPageWikiLink Carl_Pomerance.
- Ruth–Aaron_pair wikiPageWikiLink Category:Prime_numbers.
- Ruth–Aaron_pair wikiPageWikiLink Consecutive.
- Ruth–Aaron_pair wikiPageWikiLink Divisor.
- Ruth–Aaron_pair wikiPageWikiLink Hank_Aaron.
- Ruth–Aaron_pair wikiPageWikiLink Home_run.
- Ruth–Aaron_pair wikiPageWikiLink Integer.
- Ruth–Aaron_pair wikiPageWikiLink Mathematician.
- Ruth–Aaron_pair wikiPageWikiLink Mathematics.
- Ruth–Aaron_pair wikiPageWikiLink Prime_factor.
- Ruth–Aaron_pair wikiPageWikiLink Prime_number.
- Ruth–Aaron_pair wikiPageWikiLink Square-free_integer.
- Ruth–Aaron_pair wikiPageWikiLink University_of_Georgia.
- Ruth–Aaron_pair wikiPageWikiLinkText "Ruth–Aaron pair".
- Ruth–Aaron_pair wikiPageWikiLinkText "Ruth–Aaron pair".
- Ruth–Aaron_pair author "Weisstein, Eric W.".
- Ruth–Aaron_pair hasPhotoCollection Ruth–Aaron_pair.
- Ruth–Aaron_pair title "Ruth-Aaron pair".
- Ruth–Aaron_pair urlname "Ruth-AaronPair".
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- Ruth–Aaron_pair wikiPageUsesTemplate Template:MathWorld.
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- Ruth–Aaron_pair wikiPageUsesTemplate Template:OEIS.
- Ruth–Aaron_pair wikiPageUsesTemplate Template:OEIS2C.
- Ruth–Aaron_pair subject Category:Prime_numbers.
- Ruth–Aaron_pair comment "In mathematics, a Ruth–Aaron pair consists of two consecutive integers (e.g.".
- Ruth–Aaron_pair label "Ruth–Aaron pair".
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- Ruth–Aaron_pair sameAs Пара_Рута_—_Аарона.
- Ruth–Aaron_pair sameAs Ruth-Aaronpar.
- Ruth–Aaron_pair sameAs Q3099291.
- Ruth–Aaron_pair sameAs Q3099291.
- Ruth–Aaron_pair sameAs 魯斯-阿倫數對.
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