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A110601
a(n) = phi(n)*tau(n)^2, where phi is Euler's totient function and tau(n) is the number of divisors of n.
2
1, 4, 8, 18, 16, 32, 24, 64, 54, 64, 40, 144, 48, 96, 128, 200, 64, 216, 72, 288, 192, 160, 88, 512, 180, 192, 288, 432, 112, 512, 120, 576, 320, 256, 384, 972, 144, 288, 384, 1024, 160, 768, 168, 720, 864, 352, 184, 1600, 378, 720, 512, 864, 208, 1152, 640
OFFSET
1,2
LINKS
Stefan Porubsky and M. G. Greening, Problem E2351, Amer. Math. Monthly, Vol. 80, No. 4 (1973), p. 436.
FORMULA
a(n) = A000010(n) * A035116(n) = A062355(n) * A000005(n). - R. J. Mathar, Jul 26 2022
Multiplicative with a(p^e) = (e+1)^2*(p-1)*p^(e-1). - Amiram Eldar, Dec 29 2022
EXAMPLE
a(4)=18 because phi(4)=2 and tau(4)=3.
MAPLE
with(numtheory): a:=n->phi(n)*tau(n)^2: seq(a(n), n=1..70);
MATHEMATICA
Table[EulerPhi[n]DivisorSigma[0, n]^2, {n, 60}] (* Harvey P. Dale, Nov 29 2011 *)
PROG
(PARI) a(n) = eulerphi(n)*numdiv(n)^2; \\ Michel Marcus, Jun 21 2017
(Magma) [EulerPhi(n)*NumberOfDivisors(n)^2: n in [1..60]]; // Vincenzo Librandi, Jun 21 2017
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Emeric Deutsch, Jul 29 2005
STATUS
approved