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%I #8 Jun 26 2024 22:09:56
%S 0,1,1,4,1,12,1,8,9,20,1,156,1,28,30,16,1,342,1,420,42,44,1,600,25,52,
%T 27,812,1,2700,1,32,66,68,70,2592,1,76,78,1640,1,5292,1,1980,2070,92,
%U 1,2352,49,2550,102,2756,1,2970,110,3192,114,116,1,223200,1,124,4032
%N a(n) = Sum_{p|n, p prime} n^omega(n/p).
%F a(p^k) = 1 for p prime and k = 1, else p^k if k >= 2. - _Wesley Ivan Hurt_, Jun 26 2024
%t Table[DivisorSum[n, n^PrimeNu[n/#] &, PrimeQ[#] &], {n, 100}]
%Y Cf. A001221 (omega), A345354, A345355.
%K nonn,easy
%O 1,4
%A _Wesley Ivan Hurt_, Feb 05 2024