OFFSET
1,2
COMMENTS
sigma(n) is the sum of the divisors of n (A000203).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
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
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Dec 25 2016
STATUS
approved