

A117295


a(n) = phi(n)*(nphi(n))


0



0, 1, 2, 4, 4, 8, 6, 16, 18, 24, 10, 32, 12, 48, 56, 64, 16, 72, 18, 96, 108, 120, 22, 128, 100, 168, 162, 192, 28, 176, 30, 256, 260, 288, 264, 288, 36, 360, 360, 384, 40, 360, 42, 480, 504, 528, 46, 512, 294, 600, 608, 672, 52, 648, 600, 768, 756, 840, 58, 704, 60
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OFFSET

0,3


COMMENTS

For n>1, a(n) is also equal to Sum_{k=1,n1} PHI(k,n)^2 where PHI(k,n) = phi(n)*mu(n/GCD(k,n))/phi(n/GCD(k,n)), and has been considered by C. Nicol under the name G(n).  Michel Marcus, Nov 11 2012


LINKS

Table of n, a(n) for n=0..60.
C. A. Nicol, On restricted partitions and a generalization of the Euler phi number and the Moebius function, PNAS September 1, 1953 vol. 39 no. 9 963968.


EXAMPLE

a(8) = phi(8)*(8phi(8)) = 4*4 = 16.


PROG

(PARI) a(n) = {return (eulerphi(n)*(neulerphi(n)))}
(PARI) a(n) = {if (n==1, return (0)); return (sum(k=1, n1, (eulerphi(n)*moebius(n/gcd(k, n))/eulerphi(n/gcd(k, n)))^2)); } \\Michel Marcus, Nov 11 2012


CROSSREFS

Sequence in context: A184396 A077764 A110794 * A235999 A093820 A095400
Adjacent sequences: A117292 A117293 A117294 * A117296 A117297 A117298


KEYWORD

nonn


AUTHOR

Luc Stevens (lms022(AT)yahoo.com), Apr 23 2006


STATUS

approved



