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 A183098 a(1) = 0, a(n) = sum of divisors d of n such that if d = Product_(i) (p_i^e_i) then all e_i are <= 1. 5
 0, 2, 3, 2, 5, 11, 7, 2, 3, 17, 11, 23, 13, 23, 23, 2, 17, 29, 19, 37, 31, 35, 23, 47, 5, 41, 3, 51, 29, 71, 31, 2, 47, 53, 47, 41, 37, 59, 55, 77, 41, 95, 43, 79, 68, 71, 47, 95, 7, 67, 71, 93, 53, 83, 71, 107, 79, 89, 59, 163, 61, 95, 94, 2, 83, 143, 67, 121, 95, 143, 71, 65, 73, 113, 98, 135, 95, 167, 79, 157, 3, 125, 83, 219, 107, 131, 119, 167, 89, 224, 111, 163, 127, 143, 119, 191, 97, 121, 146, 87 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = sum of non-powerful divisors d of n where powerful numbers are numbers from A001694(m) for m >=2. Sequence is not the same as A183101(n): a(72) = 65, A183101(72) = 137. LINKS Antti Karttunen, Table of n, a(n) for n = 1..16385 FORMULA a(n) = A000203(n) - A183097(n) = A183100(n) - 1. a(1) = 0, a(p) = p, a(pq) = p+q+pq, a(pq...z) = [(p+1)*(q+1)*…*(z+1)]-1, a(p^k) = p, 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 {2, 3, 6, 12}; a(12) = 2+3+6+12 = 23. PROG (PARI) A183098(n) = sumdiv(n, d, d*(!ispowerful(d))); \\ Antti Karttunen, Oct 07 2017 CROSSREFS Cf. A000203, A001694, A183097, A183100, A183101, A183103. Sequence in context: A296662 A059098 A082050 * A183101 A285309 A250096 Adjacent sequences:  A183095 A183096 A183097 * A183099 A183100 A183101 KEYWORD nonn AUTHOR Jaroslav Krizek, Dec 25 2010 STATUS approved

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Last modified February 22 07:46 EST 2020. Contains 332118 sequences. (Running on oeis4.)