

A183099


a(n) = sum of powerful divisors d (excluding 1) of n.


2



0, 0, 0, 4, 0, 0, 0, 12, 9, 0, 0, 4, 0, 0, 0, 28, 0, 9, 0, 4, 0, 0, 0, 12, 25, 0, 36, 4, 0, 0, 0, 60, 0, 0, 0, 49, 0, 0, 0, 12, 0, 0, 0, 4, 9, 0, 0, 28, 49, 25, 0, 4, 0, 36, 0, 12, 0, 0, 0, 4, 0, 0, 9, 124, 0, 0, 0, 4, 0, 0, 0, 129, 0, 0, 25, 4, 0, 0, 0, 28, 117, 0, 0, 4, 0, 0, 0, 12, 0, 9, 0, 4, 0, 0, 0, 60, 0, 49, 9, 129
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OFFSET

1,4


COMMENTS

a(n) = sum of divisors d of n from set A001694(m)  powerful numbers for m >=2.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16385
Index entries for sequences related to sums of divisors


FORMULA

a(n) = A000203(n)  A183100(n) = A183097(n)  1.
a(1) = 0, a(p) = 0, a(pq) = 0, a(pq...z) = 0, a(p^k) = ((p^(k+1)1) / (p1))p1, for p, q = primes, k = natural numbers, pq...z = product of k (k > 2) distinct primes p, q, ..., z.


EXAMPLE

For n = 12, set of such divisors is {4}; a(12) = 4.


PROG

(PARI) A183099(n) = (sumdiv(n, d, ispowerful(d)*d)  1); \\ Antti Karttunen, Oct 07 2017


CROSSREFS

Cf. A000203, A001694, A183097, A183100.
Sequence in context: A236379 A126849 A284117 * A162296 A169773 A236380
Adjacent sequences: A183096 A183097 A183098 * A183100 A183101 A183102


KEYWORD

nonn


AUTHOR

Jaroslav Krizek, Dec 25 2010


STATUS

approved



