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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
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, 173, 91, 261, 1, 361, 1, 341, 130, 293, 74, 565, 1, 365, 178, 589, 1, 673, 1, 621, 331, 533, 1, 1021, 50, 729, 298, 861, 1, 1093, 146, 1093, 370, 845, 1, 1669, 1, 965
OFFSET
1,4
COMMENTS
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).
FORMULA
Sum_{k=1..n} a(k) ~ A286229 * A000330(n).
EXAMPLE
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.
PROG
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, sum(j=1, f[k, 2], n^2 / f[k, 1]^(2*j)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Daniel Suteu, Dec 22 2018
STATUS
approved