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%I #6 Aug 06 2024 02:09:17
%S 1,4,10,24,43,98,160,286,439,692,956,2948,4953,7154,9580,13030,16497,
%T 25796,35114,52432,70191,88434,106700,456742,806909,1157752,1509324,
%U 1882848,2256401,3439954,4623538,5839890,7057331,8275928,9495750,20793268,32090823,43389822
%N a(n) = Sum_{k<=n} A007955(k) * A000027(n-k+1) = Sum_{k<=n} A007955(k) * (n-k+1), where A007955(m) = product of divisors of m.
%e For n = 4, A007955(n) = b(n): a(4) = b(1)*4 + b(2)*3 + b(3)* 2 + b(4)*1 = 1*4 + 2*3 + 3*2 + 8*1 = 24.
%t a[n_] := Sum[k^(DivisorSigma[0, k]/2) * (n-k+1), {k, 1, n}]; Array[a, 50] (* _Amiram Eldar_, Aug 06 2024 *)
%Y Cf. A000027, A007955.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Apr 02 2010
%E More terms from _Amiram Eldar_, Aug 06 2024