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A183100
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a(n) = sum of divisors d of n which are either 1 or of the form Product_(i) (p_i^e_i) where the e_i are <= 1.
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3
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1, 3, 4, 3, 6, 12, 8, 3, 4, 18, 12, 24, 14, 24, 24, 3, 18, 30, 20, 38, 32, 36, 24, 48, 6, 42, 4, 52, 30, 72, 32, 3, 48, 54, 48, 42, 38, 60, 56, 78, 42, 96, 44, 80, 69, 72, 48, 96, 8, 68, 72, 94, 54, 84, 72, 108, 80, 90, 60, 164, 62, 96, 95, 3, 84, 144, 68, 122, 96, 144, 72, 66, 74, 114, 99, 136, 96, 168, 80, 158, 4, 126, 84, 220, 108, 132, 120, 168, 90, 225, 112, 164, 128, 144, 120, 192, 98, 122, 147, 88
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OFFSET
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1,2
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COMMENTS
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a(n) = sum of non-powerful divisors d of n where powerful numbers are numbers from A001694(m) for m >=1.
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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) A183099(n) = A183098(n) + 1.
a(1) = 1, a(p) = p+1, a(pq) = (p+1)*(q+1), a(pq...z) = (p+1)*(q+1)*…*(z+1), a(p^k) = 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 {1, 2, 3, 6, 12}; a(12) = 1+2+3+6+12 = 24.
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CROSSREFS
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Sequence in context: A218789 A048250 A073181 * A046897 A109506 A000113
Adjacent sequences: A183097 A183098 A183099 * A183101 A183102 A183103
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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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