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A062569 a(n) = sigma(n!).

%I A062569 #60 Jan 23 2023 09:11:24
%S A062569 1,1,3,12,60,360,2418,19344,159120,1481040,15334088,184009056,
%T A062569 2217441408,31044179712,442487616480,6686252969760,107004539285280,
%U A062569 1926081707135040,34683832925921088,693676658518421760,13891399238731734720,292460416142501376000
%N A062569 a(n) = sigma(n!).
%D A062569 Wacław Sierpiński, Elementary Theory of Numbers, Ex. 6, p. 169, Warsaw, 1964.
%H A062569 Paul D. Hanna, <a href="/A062569/b062569.txt">Table of n, a(n) for n = 0..300</a>
%H A062569 Rafael Jakimczuk, <a href="https://doi.org/10.12988/imf.2017.71088">Two topics in number theory: sum of divisors of the factorial and a formula for primes</a>, International Mathematical Forum, Vol. 12, No. 19 (2017), pp. 929-935. See Theorem 1.4, p. 932.
%H A062569 Vaclav Kotesovec, <a href="/A062569/a062569.jpg">Plot of a(n)/(n!*log(n)) for n = 2..50000</a>.
%F A062569 a(n) = A000203(A000142(n)). - _Michel Marcus_, Jan 10 2015
%F A062569 a(p) = (p+1)*a(p-1) for p prime. - _Altug Alkan_, Jul 18 2016
%F A062569 Limit_{n->oo} a(n)/n! = oo. Proof in Sierpiński. - _Bernard Schott_, Feb 09 2019
%F A062569 a(n) ~ c * n! * log(n) * (1 + O(1/log(n))), where c =  exp(gamma) = A073004 (Jakimczuk, 2017). - _Amiram Eldar_, Nov 07 2020
%e A062569 a(4) = 60, since the sum of the positive divisors of 4! is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60. - _Timothy L. Tiffin_, Jan 22 2023
%p A062569 with(numtheory):seq(sigma(n!), n=0..19); # _Zerinvary Lajos_, Feb 15 2008
%t A062569 Array[DivisorSigma[1,#! ]&,33,1] (* _Vladimir Joseph Stephan Orlovsky_, Nov 01 2009 *)
%o A062569 (PARI) for(n=0,21,print(sigma(n!)))
%o A062569 (Sage) [sigma(ZZ(n).factorial(), 1) for n in range(20)]  # _Zerinvary Lajos_, Jun 13 2009
%Y A062569 Cf. A000142, A000203, A027423, A073004.
%K A062569 easy,nonn
%O A062569 0,3
%A A062569 _Jason Earls_, Jul 03 2001