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A108639 a(n) = Sum_{k=1..n} sigma_{n-k}(k), where sigma_m(k) = Sum_{j|k} j^m.

%I A108639 #26 Oct 18 2023 02:13:54
%S A108639 1,3,6,13,29,77,229,771,2863,11573,50365,234161,1156039,6031751,
%T A108639 33130187,190929778,1151198268,7243777234,47462906927,323188163753,
%U A108639 2282922216819,16701529748621,126359471558613,987316752551419
%N A108639 a(n) = Sum_{k=1..n} sigma_{n-k}(k), where sigma_m(k) = Sum_{j|k} j^m.
%C A108639 Row sums of number triangle A109974. - _Paul Barry_, Jul 06 2005
%H A108639 Michael De Vlieger, <a href="/A108639/b108639.txt">Table of n, a(n) for n = 1..599</a>
%e A108639 a(5) = 1^4 + (1^3 + 2^3) + (1^2 + 3^2) + (1^1 + 2^1 + 4^1) + (1^0 + 5^0) = 1 + 1 + 8 + 1 + 9 + 1 + 2 + 4 + 1 + 1 = 29.
%p A108639 with(numtheory): s:=proc(n,k) local div: div:=divisors(n): sum(div[j]^k,j=1..tau(n)) end: a:=n->sum(s(i,n-i),i=1..n): seq(a(n),n=1..27); # _Emeric Deutsch_, Jul 13 2005
%t A108639 Array[Sum[DivisorSigma[# - k, k], {k, #}] &, 24] (* _Michael De Vlieger_, Dec 23 2017 *)
%o A108639 (PARI) a(n) = sum(k=1, n, sigma(k, n-k)); \\ _Michel Marcus_, Dec 24 2017
%o A108639 (Magma)
%o A108639 A108639:= func< n | (&+[DivisorSigma(j, n-j): j in [0..n-1]]) >;
%o A108639 [A108639(n): n in [1..30]]; // _G. C. Greubel_, Oct 18 2023
%o A108639 (SageMath)
%o A108639 def A108639(n): return sum(sigma(n-j, j) for j in range(n))
%o A108639 [A108639(n) for n in range(1,31)] # _G. C. Greubel_, Oct 18 2023
%Y A108639 Cf. A109974, A245466 (with k instead of n-k).
%K A108639 nonn
%O A108639 1,2
%A A108639 _Leroy Quet_, Jul 06 2005
%E A108639 More terms from _Emeric Deutsch_, Jul 13 2005
%E A108639 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, Jun 08 2007