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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 (list; graph; refs; listen; history; text; internal format)
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).

LINKS

Table of n, a(n) for n=1..62.

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

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

CROSSREFS

Cf. A001222, A095112, A286229.

Sequence in context: A276738 A094049 A286254 * A286457 A327766 A147348

Adjacent sequences:  A322661 A322662 A322663 * A322665 A322666 A322667

KEYWORD

nonn

AUTHOR

Daniel Suteu, Dec 22 2018

STATUS

approved

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Last modified April 16 04:49 EDT 2021. Contains 343030 sequences. (Running on oeis4.)