A351246 a(n) = n^6 * Sum_{p|n, p prime} 1/p^6.

0, 1, 1, 64, 1, 793, 1, 4096, 729, 15689, 1, 50752, 1, 117713, 16354, 262144, 1, 578097, 1, 1004096, 118378, 1771625, 1, 3248128, 15625, 4826873, 531441, 7533632, 1, 12437281, 1, 16777216, 1772290, 24137633, 133274, 36998208, 1, 47045945, 4827538, 64262144, 1, 93342313

Offset: 1

Author

Wesley Ivan Hurt, Feb 05 2022

Keywords

• nonn

Comments

Dirichlet convolution of A010051(n) and n^6. - Wesley Ivan Hurt, Jul 15 2025

Examples

			a(6) = 793; a(6) = 6^6 * Sum_{p|6, p prime} 1/p^6 = 46656 * (1/2^6 + 1/3^6) = 793.
		

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), this sequence (k=6), A351247 (k=7), A351248 (k=8), A351249 (k=9), A351262 (k=10).

Cf. A000040, A001221, A010051, A069091.

Programs

Mathematica

Array[#^6*DivisorSum[#, 1/#^6 &, PrimeQ] &, 50] (* Wesley Ivan Hurt, Jul 15 2025 *)

Formula

a(A000040(n)) = 1.

a(n) = Sum_{d|n} A069091(d)*A001221(n/d). - Ridouane Oudra, Jul 14 2025

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

a(n) = Sum_{d|n} c(d) * (n/d)^6, where c = A010051.

a(p^k) = p^(6*k-6) for p prime and k>=1. (End)