A022157 a(n) = n^2 - phi(n)*tau(n)^2.

0, 0, 1, -2, 9, 4, 25, 0, 27, 36, 81, 0, 121, 100, 97, 56, 225, 108, 289, 112, 249, 324, 441, 64, 445, 484, 441, 352, 729, 388, 841, 448, 769, 900, 841, 324, 1225, 1156, 1137, 576, 1521, 996, 1681, 1216, 1161, 1764, 2025, 704, 2023, 1780

Offset

1,4

Comments

An example of a sequence constructed from an arithmetic inequality.

Links

T. D. Noe, Table of n, a(n) for n = 1..2000

S. Porubsky and M. G. Greening, Problem E2351, Amer. Math. Monthly, 80, 1973, p. 436.

Formula

a(n) >= 0 for all n except for n = 4.

a(n) = 0 if and only if n is one of 1, 2, 8, 12.

Maple

with(numtheory); [ seq(n^2-phi(n)*tau(n)^2, n=1..100) ];

Mathematica

Table[n^2 - EulerPhi[n]DivisorSigma[0, n]^2, {n, 50}] (* Harvey P. Dale, Apr 12 2013 *)

Prog

(PARI) a(n) = n^2 - eulerphi(n)*numdiv(n)^2; \\ Michel Marcus, Jun 21 2017
(Magma) [n^2-EulerPhi(n)*NumberOfDivisors(n)^2: n in [1..60]]; // Vincenzo Librandi, Jun 21 2017
(GAP) List([1..50], n->n^2-Phi(n)*Tau(n)^2); # Muniru A Asiru, Sep 29 2018

Crossrefs

Cf. A110601.

Sequence in context: A228967 A342661 A213821 * A065599 A171228 A328618

Adjacent sequences: A022154 A022155 A022156 * A022158 A022159 A022160

Keyword

sign,easy,nice

Author

N. J. A. Sloane

Status

approved