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 A178637 a(n) = sum of divisors d of n such that d is not equal to p^k where p = prime, k >=1. 2
 1, 1, 1, 1, 1, 7, 1, 1, 1, 11, 1, 19, 1, 15, 16, 1, 1, 25, 1, 31, 22, 23, 1, 43, 1, 27, 1, 43, 1, 62, 1, 1, 34, 35, 36, 73, 1, 39, 40, 71, 1, 84, 1, 67, 61, 47, 1, 91, 1, 61, 52, 79, 1, 79, 56, 99, 58, 59, 1, 154, 1, 63, 85, 1, 66, 128, 1, 103, 70, 130, 1, 169, 1, 75, 91, 115, 78, 150, 1, 151, 1, 83, 1, 208, 86, 87, 88, 155, 1, 215, 92, 139, 94, 95, 96, 187, 1, 113, 133, 181 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA a(n) = A000203(n) - A023889(n) = A035321(n) + 1. a(1) = 1, a(p) = 1, a(pq) = pq+1, a(pq...z) = [(p+1)*(q+1)*…*(z+1)] - (p+q+...+z), a(p^k) = 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 {1, 6, 12}; a(12) = 1+6+12=19. PROG (PARI) A178637(n) = sumdiv(n, d, (omega(d)!=1)*(d)); \\ Antti Karttunen, Aug 06 2018 CROSSREFS One more than A035321. Sequence in context: A284118 A165725 A214685 * A295294 A317936 A277875 Adjacent sequences:  A178634 A178635 A178636 * A178638 A178639 A178640 KEYWORD nonn AUTHOR Jaroslav Krizek, Dec 25 2010 STATUS approved

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Last modified September 20 20:12 EDT 2019. Contains 327247 sequences. (Running on oeis4.)