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.

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

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

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

Cf. A000005, A000010, A035116, A062355.

Sequence in context: A312824 A312825 A312826 * A371412 A107926 A174741

Adjacent sequences: A110598 A110599 A110600 * A110602 A110603 A110604

Keyword

nonn,mult

Author

Emeric Deutsch, Jul 29 2005

Status

approved