A351197 Sum of the 9th powers of the primes dividing n.

0, 512, 19683, 512, 1953125, 20195, 40353607, 512, 19683, 1953637, 2357947691, 20195, 10604499373, 40354119, 1972808, 512, 118587876497, 20195, 322687697779, 1953637, 40373290, 2357948203, 1801152661463, 20195, 1953125, 10604499885, 19683, 40354119, 14507145975869, 1973320, 26439622160671, 512, 2357967374

Offset

1,2

Links

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

Formula

a(n) = Sum_{p|n, p prime} p^9.

G.f.: Sum_{k>=1} prime(k)^9 * x^prime(k) / (1 - x^prime(k)). - Ilya Gutkovskiy, Feb 16 2022

Additive with a(p^e) = p^9. - Amiram Eldar, Jun 20 2022

Mathematica

Array[DivisorSum[#, #^9 &, PrimeQ] &, 50]
f[p_, e_] := p^9; a[n_] := Plus @@ f @@@ FactorInteger[n]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jun 20 2022 *)

Prog

(Python)
from sympy import primefactors
def A351197(n): return sum(p**9 for p in primefactors(n)) # Chai Wah Wu, Feb 05 2022

Crossrefs

Sum of the k-th powers of the primes dividing n for k=0..10 : A001221 (k=0), A008472 (k=1), A005063 (k=2), A005064 (k=3), A005065 (k=4), A351193 (k=5), A351194 (k=6), A351195 (k=7), A351196 (k=8), this sequence (k=9), A351198 (k=10).

Sequence in context: A254299 A283340 A321833 * A017682 A001017 A352055

Adjacent sequences: A351194 A351195 A351196 * A351198 A351199 A351200

Keyword

nonn

Author

Wesley Ivan Hurt, Feb 04 2022

Status

approved