A351249 - OEIS

%I #9 Feb 06 2022 01:35:06

%S 0,1,1,512,1,20195,1,262144,19683,1953637,1,10339840,1,40354119,

%T 1972808,134217728,1,397498185,1,1000262144,40373290,2357948203,1,

%U 5293998080,1953125,10604499885,387420489,20661308928,1,39453437071,1,68719476736,2357967374,118587877009,42306732

%N a(n) = n^9 * Sum_{p|n, p prime} 1/p^9.

%F a(A000040(n)) = 1.

%e a(6) = 20195; a(6) = 6^9 * Sum_{p|6, p prime} 1/p^9 = 10077696 * (1/2^9 + 1/3^9) = 20195.

%o (Python)

%o from sympy import primefactors

%o def A351249(n): return sum((n//p)**9 for p in primefactors(n)) # _Chai Wah Wu_, Feb 05 2022

%Y 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), A351247 (k=7), A351248 (k=8), this sequence (k=9), A351262 (k=10).

%Y Cf. A000040.

%K nonn

%O 1,4

%A _Wesley Ivan Hurt_, Feb 05 2022