

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
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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



