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A056218
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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].
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3
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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
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OFFSET
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0,5
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REFERENCES
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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.
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LINKS
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EXAMPLE
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a(6) = 6!/(2!*3!) = 720/(2*6) = 60 because 2*3 is the prime factorization of 6.
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MATHEMATICA
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{1}~Join~Array[#!/Times @@ Map[(#1!)^#2 & @@ # &, FactorInteger[#]] &, 60] (* Michael De Vlieger, Mar 24 2024 *)
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CROSSREFS
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Cf. A075072 (distinct prime factors).
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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