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- Prime_signature abstract "The prime signature of a number is the multiset of exponents of its prime factorisation.For example, all prime numbers have a prime signature of {1}, the squares of primes have a prime signature of {2}, the products of 2 distinct primes have a prime signature of {1,1} and the products of a square of a prime and a different prime (e.g. 12,18,20,... ) have a prime signature of {2,1}.The number of divisors that a number has is determined by its prime signature as follows: If you add one to each exponent and multiply them together you get the number of divisors including the number itself and 1. For example, 20 has prime signature {2,1} and so the number of divisors is 3 × 2 = 6. They are 1, 2, 4, 5, 10 and 20.The smallest number of each prime signature is a product of primorials. The first few are:1, 2, 4, 6, 8, 12, 16, 24, 30, 32, 36, 48, 60, 64, 72, 96, 120, 128, 144, 180, 192, 210, 216, ... (sequence A025487 in OEIS).The divisor function τ(n), the Möbius function μ(n), the number of distinct prime divisors ω(n) of n, the number of prime divisors Ω(n) of n, the indicator function of the squarefree integers, and many other important functions in number theory, are functions of the prime signature of n.".
- Prime_signature wikiPageExternalLink primesiglist.htm.
- Prime_signature wikiPageExternalLink primesigmap.htm.
- Prime_signature wikiPageID "2715150".
- Prime_signature wikiPageLength "3429".
- Prime_signature wikiPageOutDegree "25".
- Prime_signature wikiPageRevisionID "548091185".
- Prime_signature wikiPageWikiLink Achilles_number.
- Prime_signature wikiPageWikiLink Almost_prime.
- Prime_signature wikiPageWikiLink Category:Number_theory.
- Prime_signature wikiPageWikiLink Category:Prime_numbers.
- Prime_signature wikiPageWikiLink Cube_(algebra).
- Prime_signature wikiPageWikiLink Divisor.
- Prime_signature wikiPageWikiLink Divisor_function.
- Prime_signature wikiPageWikiLink Empty_product.
- Prime_signature wikiPageWikiLink Fundamental_theorem_of_arithmetic.
- Prime_signature wikiPageWikiLink Indicator_function.
- Prime_signature wikiPageWikiLink Integer_factorization.
- Prime_signature wikiPageWikiLink Multiset.
- Prime_signature wikiPageWikiLink Möbius_function.
- Prime_signature wikiPageWikiLink On-Line_Encyclopedia_of_Integer_Sequences.
- Prime_signature wikiPageWikiLink Powerful_number.
- Prime_signature wikiPageWikiLink Prime_number.
- Prime_signature wikiPageWikiLink Primorial.
- Prime_signature wikiPageWikiLink Semiprime.
- Prime_signature wikiPageWikiLink Sphenic_number.
- Prime_signature wikiPageWikiLink Square-free_integer.
- Prime_signature wikiPageWikiLink Square_(algebra).
- Prime_signature wikiPageWikiLink Square_number.
- Prime_signature wikiPageWikiLinkText "Prime signature".
- Prime_signature title "Prime Signature".
- Prime_signature urlname "PrimeSignature".
- Prime_signature wikiPageUsesTemplate Template:Mathworld.
- Prime_signature wikiPageUsesTemplate Template:OEIS.
- Prime_signature wikiPageUsesTemplate Template:OEIS_link.
- Prime_signature subject Category:Number_theory.
- Prime_signature subject Category:Prime_numbers.
- Prime_signature hypernym Multiset.
- Prime_signature type Field.
- Prime_signature comment "The prime signature of a number is the multiset of exponents of its prime factorisation.For example, all prime numbers have a prime signature of {1}, the squares of primes have a prime signature of {2}, the products of 2 distinct primes have a prime signature of {1,1} and the products of a square of a prime and a different prime (e.g. 12,18,20,...".
- Prime_signature label "Prime signature".
- Prime_signature sameAs Q7243382.
- Prime_signature sameAs m.07zncz.
- Prime_signature sameAs Q7243382.
- Prime_signature wasDerivedFrom Prime_signature?oldid=548091185.
- Prime_signature isPrimaryTopicOf Prime_signature.