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A061555
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Integer part of sigma(n!)/n!.
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1
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1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8
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OFFSET
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0,4
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COMMENTS
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With increasing n, a(n) goes to infinity (proof in Sierpiński).
It seems that sigma(n!)/n! is an integer only for n = 0, 1, 3, 5 and corresponding values are 1, 1, 2, 3.
For m >= 2, the smallest integer n such that a(n) = m is A061556(m). (End)
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REFERENCES
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Wacław Sierpiński, Elementary Theory of Numbers, Ex. 6, p. 169, Warsaw, 1964.
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LINKS
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FORMULA
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MATHEMATICA
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Table[Floor[DivisorSigma[1, n!]/n!], {n, 0, 100}] (* Wesley Ivan Hurt, Apr 16 2024 *)
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PROG
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(PARI) { for (n=0, 1000, write("b061555.txt", n, " ", sigma(n!)\n!) ) } \\ Harry J. Smith, Jul 24 2009
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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