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
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.
Crossrefs
Cf. A110601.
Programs
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GAP
List([1..50],n->n^2-Phi(n)*Tau(n)^2); # Muniru A Asiru, Sep 29 2018
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Magma
[n^2-EulerPhi(n)*NumberOfDivisors(n)^2: n in [1..60]]; // Vincenzo Librandi, Jun 21 2017
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Maple
with(numtheory); [ seq(n^2-phi(n)*tau(n)^2,n=1..100) ];
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Mathematica
Table[n^2 - EulerPhi[n]DivisorSigma[0, n]^2, {n, 50}] (* Harvey P. Dale, Apr 12 2013 *) -
PARI
a(n) = n^2 - eulerphi(n)*numdiv(n)^2; \\ Michel Marcus, Jun 21 2017
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.
Comments