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Sum of squares of divisors of n!.
1

%I #18 Dec 07 2019 12:18:25

%S 1,1,5,50,850,22100,806806,40340300,2584263500,209609328500,

%T 20993420690550,2561197324247100,368819285671473000,

%U 62699278564150410000,12294076739210974071000,2766341857504878226501200

%N Sum of squares of divisors of n!.

%C See also A062569 sigma_1(n!).

%H Amiram Eldar, <a href="/A116906/b116906.txt">Table of n, a(n) for n = 0..253</a>

%F a(n) = A001157(A000142(n)).

%F a(n) = Sum_{d|n!} d^2.

%F a(n) = sigma_2(n!).

%e a(0) = 1 because only 1 divides 0! = 1.

%e a(1) = 1 because only 1 divides 1! = 1.

%e a(2) = 5 because both 1 and 2 divide 2! = 2 and 1^2 + 2^2 = 5.

%e a(3) = 50 because 1, 2, 3, 6 divide 3! = 6 and 1^2 + 2^2 + 3^2 + 6^2 = 50.

%e 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.

%t a[n_] := DivisorSigma[2, n!]; Array[a, 16, 0] (* _Amiram Eldar_, Aug 01 2019 *)

%o (Sage) [sigma(factorial(n),2)for n in range(0,16)] # _Zerinvary Lajos_, Jun 13 2009

%Y Cf. A000142, A000203, A001157, A062569.

%K easy,nonn

%O 0,3

%A _Jonathan Vos Post_, Mar 15 2006