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Sum_{k<=n} (sigma(k)^2), where sigma(k) denotes the sum of the divisors of k A000203.
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%I #17 Jul 09 2024 09:56:29

%S 1,10,26,75,111,255,319,544,713,1037,1181,1965,2161,2737,3313,4274,

%T 4598,6119,6519,8283,9307,10603,11179,14779,15740,17504,19104,22240,

%U 23140,28324,29348,33317,35621,38537,40841,49122,50566,54166,57302

%N Sum_{k<=n} (sigma(k)^2), where sigma(k) denotes the sum of the divisors of k A000203.

%H Vaclav Kotesovec, <a href="/A072379/b072379.txt">Table of n, a(n) for n = 1..10000</a>

%F Ramanujan's asymptotic formula: (5/6)*Zeta(3)*n^3+O(n^2*log(n)^2)

%p A072379 := proc(n)

%p add( numtheory[sigma](k)^2,k=0..n) ;

%p end proc:

%p seq(A072379(n),n=1..80) ; # _R. J. Mathar_, Jul 09 2024

%t Accumulate[Table[DivisorSigma[1, k]^2, {k, 1, 50}]] (* _Vaclav Kotesovec_, Sep 10 2018 *)

%o (PARI) a(n) = sum(k=1, n, sigma(k)^2) \\ _Michel Marcus_, Jun 20 2013

%Y Cf. A024916, A072861.

%Y Cf. A057434, A061502, A074789.

%K nonn

%O 1,2

%A Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jul 20 2002