

A069088


Sum(dn, core(d) ) where d are the divisors of n and where core(d) is the squarefree part of d: the smallest number such that d*core(d) is a square.


2



1, 3, 4, 4, 6, 12, 8, 6, 5, 18, 12, 16, 14, 24, 24, 7, 18, 15, 20, 24, 32, 36, 24, 24, 7, 42, 8, 32, 30, 72, 32, 9, 48, 54, 48, 20, 38, 60, 56, 36, 42, 96, 44, 48, 30, 72, 48, 28, 9, 21, 72, 56, 54, 24, 72, 48, 80, 90, 60, 96, 62, 96, 40, 10, 84, 144, 68, 72, 96, 144, 72, 30, 74
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Multiplicative because it is the Inverse Moebius transform of A007913 which is multiplicative.  Christian G. Bower, May 17 2005.


LINKS

Table of n, a(n) for n=1..73.


FORMULA

G.f.: sum(k>=1, core(k)*x^k/(1x^k)).  Benoit Cloitre, Apr 21 2003
Dirichlet g.f. zeta(2*s)*zeta(s)*zeta(s1)/zeta(2*s2).  R. J. Mathar, Oct 31 2011


PROG

(PARI) a(n) = sumdiv(n, d, core(d) );


CROSSREFS

Cf. A007913.
Sequence in context: A086659 A265887 A008473 * A178450 A019462 A078071
Adjacent sequences: A069085 A069086 A069087 * A069089 A069090 A069091


KEYWORD

easy,nonn,mult


AUTHOR

Benoit Cloitre, Apr 05 2002


STATUS

approved



