A225983 Numbers k such that gcd(phi(k), tau(k)) = 1.

1, 2, 4, 16, 25, 64, 81, 100, 121, 256, 289, 484, 529, 729, 841, 1024, 1156, 1296, 1600, 1681, 2116, 2209, 2401, 2809, 3025, 3364, 3481, 4096, 4624, 5041, 5184, 6400, 6724, 6889, 7225, 7744, 7921, 8464, 8836, 10201, 11236, 11449, 11664, 12100, 12769, 13225

Offset: 1

Author

Paolo P. Lava, May 22 2013

Keywords

• nonn

Examples

			If n = 13924 then phi(n) = 6844 = 2^2*29*59 and tau(n) = 9 = 3^2. There is no common prime factor.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..100 from Paolo P. Lava, terms 101..1000 from T. D. Noe)

Crossrefs

Cf. A000005, A000010, A046678, A055008.

Programs

Maple

with(numtheory); A225983:=proc(q) local n;
for n from 1 to q do if gcd(tau(n),phi(n))=1 then print(n);
fi; od; end: A225983(10^6);

Mathematica

t = {}; n = 0; While[Length[t] < 100, n++; If[GCD[EulerPhi[n], DivisorSigma[0, n]] == 1, AppendTo[t, n]]]; t (* T. D. Noe, May 22 2013 *)