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A116906
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Sum of squares of divisors of n!.
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1
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1, 1, 5, 50, 850, 22100, 806806, 40340300, 2584263500, 209609328500, 20993420690550, 2561197324247100, 368819285671473000, 62699278564150410000, 12294076739210974071000, 2766341857504878226501200
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{d|n!} d^2.
a(n) = sigma_2(n!).
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EXAMPLE
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a(0) = 1 because only 1 divides 0! = 1.
a(1) = 1 because only 1 divides 1! = 1.
a(2) = 5 because both 1 and 2 divide 2! = 2 and 1^2 + 2^2 = 5.
a(3) = 50 because 1, 2, 3, 6 divide 3! = 6 and 1^2 + 2^2 + 3^2 + 6^2 = 50.
a(4) = 850 because 1, 2, 3, 4, 6, 8, 12, 24 divide 4! = 24 and 1^2 + 2^2 + 3^2 + 4^2 + 6^2 + 8^2 + 12^2 + 24^2 = 850.
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MATHEMATICA
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a[n_] := DivisorSigma[2, n!]; Array[a, 16, 0] (* Amiram Eldar, Aug 01 2019 *)
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PROG
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(Sage) [sigma(factorial(n), 2)for n in range(0, 16)] # Zerinvary Lajos, Jun 13 2009
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CROSSREFS
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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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