cp's OEIS Frontend

A072379 Sum_{k<=n} (sigma(k)^2), where sigma(k) denotes the sum of the divisors of k A000203.

%I A072379 #17 Jul 09 2024 09:56:29
%S A072379 1,10,26,75,111,255,319,544,713,1037,1181,1965,2161,2737,3313,4274,
%T A072379 4598,6119,6519,8283,9307,10603,11179,14779,15740,17504,19104,22240,
%U A072379 23140,28324,29348,33317,35621,38537,40841,49122,50566,54166,57302
%N A072379 Sum_{k<=n} (sigma(k)^2), where sigma(k) denotes the sum of the divisors of k A000203.
%H A072379 Vaclav Kotesovec, <a href="/A072379/b072379.txt">Table of n, a(n) for n = 1..10000</a>
%F A072379 Ramanujan's asymptotic formula: (5/6)*Zeta(3)*n^3+O(n^2*log(n)^2)
%p A072379 A072379 := proc(n)
%p A072379     add( numtheory[sigma](k)^2,k=0..n) ;
%p A072379 end proc:
%p A072379 seq(A072379(n),n=1..80) ; # _R. J. Mathar_, Jul 09 2024
%t A072379 Accumulate[Table[DivisorSigma[1, k]^2, {k, 1, 50}]] (* _Vaclav Kotesovec_, Sep 10 2018 *)
%o A072379 (PARI) a(n) = sum(k=1, n, sigma(k)^2) \\ _Michel Marcus_, Jun 20 2013
%Y A072379 Cf. A024916, A072861.
%Y A072379 Cf. A057434, A061502, A074789.
%K A072379 nonn
%O A072379 1,2
%A A072379 Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jul 20 2002