

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
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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



