OFFSET
1,2
COMMENTS
Inverse Möbius transform of n^9 * c(n), where c(n) is the prime characteristic (A010051). - Wesley Ivan Hurt, Jun 22 2024
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
a(n) = Sum_{d|n} d^9 * c(d), where c = A010051. - Wesley Ivan Hurt, Jun 22 2024
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Feb 04 2022
STATUS
approved