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A023889 Sum of prime power divisors of n (not including 1). 10
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 * A327669 A253413 A093783

Adjacent sequences:  A023886 A023887 A023888 * A023890 A023891 A023892

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified June 5 12:47 EDT 2020. Contains 334840 sequences. (Running on oeis4.)