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A183099
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a(n) = sum of powerful divisors d (excluding 1) of n.
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1
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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
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1,4
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COMMENTS
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a(n) = sum of divisors d of n from set A001694(m) - powerful numbers for m >=2.
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LINKS
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Table of n, a(n) for n=1..100.
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FORMULA
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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.
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EXAMPLE
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For n = 12, set of such divisors is {4}; a(12) = 4.
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CROSSREFS
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Sequence in context: A046782 A074037 A126849 * A162296 A169773 A169765
Adjacent sequences: A183096 A183097 A183098 * A183100 A183101 A183102
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KEYWORD
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nonn
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AUTHOR
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Jaroslav Krizek, Dec 25 2010
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STATUS
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approved
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