A280077 Partial sums of A007429 (Sum_{d|n} sigma(d)).

1, 5, 10, 21, 28, 48, 57, 83, 101, 129, 142, 197, 212, 248, 283, 340, 359, 431, 452, 529, 574, 626, 651, 781, 819, 879, 937, 1036, 1067, 1207, 1240, 1360, 1425, 1501, 1564, 1762, 1801, 1885, 1960, 2142, 2185, 2365, 2410, 2553, 2679, 2779, 2828, 3113, 3179

Offset: 1

Author

Jaroslav Krizek, Dec 25 2016

Keywords

• nonn

Comments

sigma(n) is the sum of the divisors of n (A000203).

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A237349 (partial sums of A211776), A280078 (partial products of A007429).

Programs

Magma

[&+[&+[SumOfDivisors(d): d in Divisors(k)]: k in [1..n]]: n in [1..100]]

PARI

a(n) = sum(k=1, n, sumdiv(k, d, sigma(d))); \\ Michel Marcus, May 29 2018

PARI

my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, sigma(k)*x^k/(1-x^k))/(1-x)) \\ Seiichi Manyama, Jul 24 2022

Formula

a(n) = Sum_{i=1..n} A007429(i).

a(n) = Sum_{k=1..n} A000203(k) * floor(n/k). - Daniel Suteu, May 28 2018

a(n) = Sum_{k=1..n} A000005(k)/2 * floor(n/k) * floor(1+n/k). - Daniel Suteu, May 28 2018

a(n) ~ Pi^4 * n^2 / 72. - Vaclav Kotesovec, Nov 06 2018

G.f.: (1/(1-x)) * Sum_{k>=1} sigma(k) * x^k/(1 - x^k). - Seiichi Manyama, Jul 24 2022