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A023889 Sum of prime power divisors of n (not including 1). 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000

FORMULA

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) = A023888(n) - 1. - Michel Marcus, Mar 21 2017

MATHEMATICA

Array[ Plus @@ (Select[ Divisors[ # ], PrimePowerQ ])&, 80 ]

PROG

(PARI) a(n) = sumdiv(n, d, if(isprimepower(d), d)); \\ Michel Marcus, Mar 21 2017; corrected by Daniel Suteu, Jul 20 2018

(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

CROSSREFS

Cf. A023888.

Sequence in context: A269374 A137761 A100769 * A253413 A093783 A096861

Adjacent sequences:  A023886 A023887 A023888 * A023890 A023891 A023892

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified April 19 08:44 EDT 2019. Contains 322241 sequences. (Running on oeis4.)