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A322664 a(n) = n^2 * Sum_{p^k|n} Sum_{j=1..k} 1/p^(2*j), where p are primes dividing n with multiplicity k. 1

%I

%S 0,1,1,5,1,13,1,21,10,29,1,61,1,53,34,85,1,121,1,141,58,125,1,253,26,

%T 173,91,261,1,361,1,341,130,293,74,565,1,365,178,589,1,673,1,621,331,

%U 533,1,1021,50,729,298,861,1,1093,146,1093,370,845,1,1669,1,965

%N a(n) = n^2 * Sum_{p^k|n} Sum_{j=1..k} 1/p^(2*j), where p are primes dividing n with multiplicity k.

%C The generalized formula is f(n,m) = n^m * Sum_{p^k|n} Sum_{j=1..k} 1/p^(m*j), where f(n,0) = A001222(n) and f(n,1) = A095112(n).

%F Sum_{k=1..n} a(k) ~ A286229 * A000330(n).

%e The prime factorization of 24 is 2^3 * 3, so a(24) = 24^2 * (1/2^2 + 1/2^(2*2) + 1/2^(2*3) + 1/3^2) = 253.

%o a(n) = my(f=factor(n)); sum(k=1, #f~, sum(j=1, f[k,2], n^2 / f[k,1]^(2*j)));

%Y Cf. A001222, A095112, A286229.

%K nonn

%O 1,4

%A _Daniel Suteu_, Dec 22 2018

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Last modified May 6 02:35 EDT 2021. Contains 343579 sequences. (Running on oeis4.)