A339308 Partial sums of products of proper divisors of n (A007956).

1, 2, 3, 5, 6, 12, 13, 21, 24, 34, 35, 179, 180, 194, 209, 273, 274, 598, 599, 999, 1020, 1042, 1043, 14867, 14872, 14898, 14925, 15709, 15710, 42710, 42711, 43735, 43768, 43802, 43837, 323773, 323774, 323812, 323851, 387851, 387852, 461940, 461941, 463877

Offset: 1

Author

Jaroslav Krizek, Nov 29 2020

Keywords

• nonn

Examples

			a(6) = 12 = (1 + 1 + 1 + 2 + 1 + 6), where pod(n)/ n = 1, 1, 1, 2, 1, 6, 1, 8, 3, 10, 1, 144, ...
		

Crossrefs

Cf. A007955 (pod(n)), A007956 (pod(n)/n), A092144 (partial products of A007956).

Programs

Magma

[&+[&*Divisors(k) / k: k in [1..n]]: n in [1..100]]

Mathematica

popd[n_] := n^(DivisorSigma[0, n]/2 - 1); Accumulate @ Array[popd, 44] (* Amiram Eldar, Nov 30 2020 *)

PARI

a(n) = sum(k=1, n, vecprod(divisors(k))/k); \\ Michel Marcus, Nov 30 2020

Formula

a(n) = Sum_{k=1..n} pod(k)/k = Sum_{k=1..n} (A007955(k)/k) = Sum_{k=1..n} A007956(k).