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A062569 a(n) = sigma(n!). 24

%I

%S 1,1,3,12,60,360,2418,19344,159120,1481040,15334088,184009056,

%T 2217441408,31044179712,442487616480,6686252969760,107004539285280,

%U 1926081707135040,34683832925921088,693676658518421760,13891399238731734720,292460416142501376000

%N a(n) = sigma(n!).

%C Lim_{n->infinity: a(n)/n! = infinity}. Proof in Sierpiński. - _Bernard Schott_, Feb 09 2019

%D Wacław Sierpiński, Elementary Theory of Numbers, Ex. 6, p. 169, Warsaw, 1964.

%H Paul D. Hanna, <a href="/A062569/b062569.txt">Table of n, a(n) for n = 0..300</a>

%H Vaclav Kotesovec, <a href="/A062569/a062569.jpg">Plot of a(n)/(n!*log(n)) for n = 2..50000</a>

%F a(n) = A000203(A000142(n)). - _Michel Marcus_, Jan 10 2015

%F a(p) = (p+1)*a(p-1) for p prime. - _Altug Alkan_, Jul 18 2016

%p with(numtheory):seq(sigma(n!), n=0..19); # _Zerinvary Lajos_, Feb 15 2008

%t Array[DivisorSigma[1,#! ]&,33,1] (* _Vladimir Joseph Stephan Orlovsky_, Nov 01 2009 *)

%o (PARI) for(n=0,21,print(sigma(n!)))

%o (Sage) [sigma(ZZ(n).factorial(), 1) for n in range(20)] # _Zerinvary Lajos_, Jun 13 2009

%Y Cf. A027423.

%K easy,nonn

%O 0,3

%A _Jason Earls_, Jul 03 2001

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Last modified August 10 08:40 EDT 2020. Contains 336369 sequences. (Running on oeis4.)