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 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 (list; graph; refs; listen; history; text; internal format)
 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 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) / (p-1))-p-1, 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

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Last modified June 17 15:38 EDT 2021. Contains 345085 sequences. (Running on oeis4.)