A056218 If n = p_1^a_1 * p_2^a_2 * p_3^a_3 * ..., where p_k is the k-th prime and the a's are nonnegative integers, then a(n) = n!/product_{k >= 1} [(p_k)!^a_k].

1, 1, 1, 1, 6, 1, 60, 1, 5040, 10080, 15120, 1, 19958400, 1, 8648640, 1816214400, 1307674368000, 1, 88921857024000, 1, 5068545850368000, 1689515283456000, 14079294028800, 1, 12926008369442488320000, 1077167364120207360000, 32382376266240000, 50411432640825704448000000

Offset

0,5

References

Amarnath Murthy, Generalization of partition function and introducing Smarandache Factor Partition, Smarandache Notions Journal, Vol. 11, 2000.

Amarnath Murthy, Length and extent of Smarandache Factor Partition, Smarandache Notions Journal, Vol. 11, 2000.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..458

Michael De Vlieger, Log log scatterplot of log_10(a(n)) for n = 1..2^12, ignoring a(n) = 1.

Example

a(6) = 6!/(2!*3!) = 720/(2*6) = 60 because 2*3 is the prime factorization of 6.

Mathematica

{1}~Join~Array[#!/Times @@ Map[(#1!)^#2 & @@ # &, FactorInteger[#]] &, 60] (* Michael De Vlieger, Mar 24 2024 *)

Crossrefs

Cf. A075072 (distinct prime factors).

Sequence in context: A339100 A344918 A174502 * A352014 A292219 A364110

Adjacent sequences: A056215 A056216 A056217 * A056219 A056220 A056221

Keyword

easy,nonn

Author

Leroy Quet, Aug 05 2000

Status

approved