A279364 Sum of 5th powers of proper divisors of n.

0, 1, 1, 33, 1, 276, 1, 1057, 244, 3158, 1, 9076, 1, 16840, 3369, 33825, 1, 67101, 1, 104182, 17051, 161084, 1, 290676, 3126, 371326, 59293, 555688, 1, 870552, 1, 1082401, 161295, 1419890, 19933, 2206525, 1, 2476132, 371537, 3336950, 1, 4646784, 1, 5315740, 821793, 6436376, 1, 9301876, 16808, 9868783

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Proper divisors.

Index entries for sequences related to sums of divisors

Formula

a(n) = 1 if n is prime.

a(p^k) = (p^(5*k) - 1)/(p^5 - 1) for p is prime.

Dirichlet g.f.: zeta(s-5)*(zeta(s) - 1).

a(n) = A001160(n) - A000584(n).

G.f.: -x*(1 + 26*x + 66*x^2 + 26*x^3 + x^4)/(1 - x)^6 + Sum_{k>=1} k^5 x^k/(1 - x^k). - Ilya Gutkovskiy, Mar 18 2017

Example

a(10) = 1^5 + 2^5 + 5^5 = 3158, because 10 has 3 proper divisors {1,2,5}.
a(11) = 1^5 = 1, because 11 has 1 proper divisor {1}.

Mathematica

Table[DivisorSigma[5, n] - n^5, {n, 50}]

Prog

(PARI) for(n=1, 50, print1(sigma(n, 5) - n^5, ", ")) \\ Indranil Ghosh, Mar 18 2017
(Python)
from sympy.ntheory import divisor_sigma
print([divisor_sigma(n, 5) - n**5 for n in range(1, 51)]) # Indranil Ghosh, Mar 18 2017

Crossrefs

Cf. A000584, A001160.

Cf. A001065, A067558, A276634, A279363.

Sequence in context: A372394 A225347 A218116 * A308408 A263169 A034060

Adjacent sequences: A279361 A279362 A279363 * A279365 A279366 A279367

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Dec 10 2016

Status

approved