A351247 a(n) = n^7 * Sum_{p|n, p prime} 1/p^7.

0, 1, 1, 128, 1, 2315, 1, 16384, 2187, 78253, 1, 296320, 1, 823671, 80312, 2097152, 1, 5062905, 1, 10016384, 825730, 19487299, 1, 37928960, 78125, 62748645, 4782969, 105429888, 1, 181139311, 1, 268435456, 19489358, 410338801, 901668, 648051840, 1, 893871867, 62750704

Offset: 1

Author

Wesley Ivan Hurt, Feb 05 2022

Keywords

• nonn

Comments

Dirichlet convolution of A010051(n) and n^7. - Wesley Ivan Hurt, Jul 15 2025

Examples

			a(6) = 2315; a(6) = 6^7 * Sum_{p|6, p prime} 1/p^7 = 279936 * (1/2^7 + 1/3^7) = 2315.
		

Links

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

Crossrefs

Sequences of the form n^k * Sum_{p|n, p prime} 1/p^k for k = 0..10: A001221 (k=0), A069359 (k=1), A322078 (k=2), A351242 (k=3), A351244 (k=4), A351245 (k=5), A351246 (k=6), this sequence (k=7), A351248 (k=8), A351249 (k=9), A351262 (k=10).

Cf. A000040, A001221, A010051, A069092.

Programs

Mathematica

Array[#^7*DivisorSum[#, 1/#^7 &, PrimeQ] &, 50] (* Wesley Ivan Hurt, Jul 15 2025 *)

Formula

a(A000040(n)) = 1.

a(n) = Sum_{d|n} A069092(d)*A001221(n/d). - Ridouane Oudra, Jul 15 2025

From Wesley Ivan Hurt, Jul 15 2025: (Start)

a(n) = Sum_{d|n} c(d) * (n/d)^7, where c = A010051.

a(p^k) = p^(7*k-7) for p prime and k>=1. (End)