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
KEYWORD
sign,easy,nice
AUTHOR
STATUS
approved