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A095112 a(n) is the sum of n/k over all prime powers k > 1 which divide n. 6
0, 1, 1, 3, 1, 5, 1, 7, 4, 7, 1, 13, 1, 9, 8, 15, 1, 17, 1, 19, 10, 13, 1, 29, 6, 15, 13, 25, 1, 31, 1, 31, 14, 19, 12, 43, 1, 21, 16, 43, 1, 41, 1, 37, 29, 25, 1, 61, 8, 37, 20, 43, 1, 53, 16, 57, 22, 31, 1, 77, 1, 33, 37, 63, 18, 61, 1, 55, 26, 59, 1, 95, 1, 39, 43, 61, 18, 71, 1, 91, 40 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A073093(n)-1 terms are added to produce a(n). - Michel Marcus, Aug 29 2013

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

a(n) = Sum_{k=1..n} bigomega(gcd(n,k)). - Lechoslaw Ratajczak, Jun 18 2017

Sum_{k=1..n} a(k) ~ A154945 * n*(n+1)/2. - Daniel Suteu, Apr 01 2019

EXAMPLE

The prime power divisors of 24 are 2, 4, 8 and 3, so a(24) = 24/2 + 24/4 + 24/8 + 24/3 = 29.

MATHEMATICA

a[n_]:=Plus@@(n/Flatten[ #[[1]]^Range[ #[[2]]]&/@FactorInteger[n]])

PROG

(PARI) A095112(n) = sumdiv(n, d, (1==omega(d))*(n/d)); \\ Antti Karttunen, Feb 25 2018

CROSSREFS

Cf. A001221, A001222, A073093.

Sequence in context: A122383 A292393 A136180 * A160596 A092319 A254938

Adjacent sequences:  A095109 A095110 A095111 * A095113 A095114 A095115

KEYWORD

nonn

AUTHOR

Dean Hickerson, following a suggestion of Leroy Quet, May 28 2004

STATUS

approved

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Last modified May 6 02:46 EDT 2021. Contains 343579 sequences. (Running on oeis4.)