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A248076 Partial sums of the sum of the 5th powers of the divisors of n: Sum_{i=1..n} sigma_5(i). 4
1, 34, 278, 1335, 4461, 12513, 29321, 63146, 122439, 225597, 386649, 644557, 1015851, 1570515, 2333259, 3415660, 4835518, 6792187, 9268287, 12572469, 16673621, 21988337, 28424681, 36677981, 46446732, 58699434, 73107634, 90873690, 111384840, 136555392 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = Sum_{i=1..n} sigma_5(i) = Sum_{i=1..n} A001160(i).

a(n) ~ Zeta(6) * n^6 / 6. - Vaclav Kotesovec, Sep 02 2018

a(n) ~ Pi^6 * n^6 / 5670. - Vaclav Kotesovec, Sep 02 2018

a(n) = Sum_{k=1..n} (Bernoulli(6, floor(1 + n/k)) - 1/42)/6, where Bernoulli(n,x) are the Bernoulli polynomials. - Daniel Suteu, Nov 07 2018

a(n) = Sum_{k=1..n} k^5 * floor(n/k). - Daniel Suteu, Nov 08 2018

MAPLE

with(numtheory): A248076:=n->add(sigma[5](i), i=1..n): seq(A248076(n), n=1..50);

MATHEMATICA

Table[Sum[DivisorSigma[5, i], {i, n}], {n, 30}]

Accumulate[DivisorSigma[5, Range[30]]] (* Vaclav Kotesovec, Mar 30 2018 *)

PROG

(PARI) lista(nn) = vector(nn, n, sum(i=1, n, sigma(i, 5))) \\ Michel Marcus, Sep 30 2014

(MAGMA) [(&+[DivisorSigma(5, j): j in [1..n]]): n in [1..30]]; // G. C. Greubel, Nov 07 2018

CROSSREFS

Cf. A001160 (sigma_5).

Cf. A024916: Partial sums of sigma(n)   = A000203(n).

Cf. A064602: Partial sums of sigma_2(n) = A001157(n).

Cf. A064603: Partial sums of sigma_3(n) = A001158(n).

Cf. A064604: Partial sums of sigma_4(n) = A001159(n).

Sequence in context: A295917 A219927 A228284 * A301543 A252999 A229327

Adjacent sequences:  A248073 A248074 A248075 * A248077 A248078 A248079

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Sep 30 2014

STATUS

approved

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Last modified June 19 19:11 EDT 2019. Contains 324222 sequences. (Running on oeis4.)