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A023889
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Sum of the prime power divisors of n (not including 1).
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11
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0, 2, 3, 6, 5, 5, 7, 14, 12, 7, 11, 9, 13, 9, 8, 30, 17, 14, 19, 11, 10, 13, 23, 17, 30, 15, 39, 13, 29, 10, 31, 62, 14, 19, 12, 18, 37, 21, 16, 19, 41, 12, 43, 17, 17, 25, 47, 33, 56, 32, 20, 19, 53, 41, 16, 21, 22, 31, 59, 14, 61, 33, 19, 126, 18, 16, 67, 23, 26, 14
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: Sum_{k>=2} floor(1/omega(k))*k*x^k/(1 - x^k), where omega(k) is the number of distinct prime factors (A001221). - Ilya Gutkovskiy, Jan 04 2017
a(n) = Sum_{d|n} d * [omega(d) = 1], where omega is the number of distinct prime factors and [ ] is the Iverson bracket. - Wesley Ivan Hurt, Jan 28 2021
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MATHEMATICA
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Array[ Plus @@ (Select[ Divisors[ # ], PrimePowerQ ])&, 80 ]
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PROG
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(PARI) a(n) = my(f = factor(n)); sum(k = 1, #f~, f[k, 1] * (f[k, 1]^f[k, 2] - 1) / (f[k, 1] - 1)) \\ Daniel Suteu, Jul 20 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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