A065149 Composite numbers m such that phi(m)*sigma(m) is divisible by m-1.

10, 33, 65, 136, 145, 261, 385, 451, 897, 946, 1281, 1441, 1665, 1729, 2241, 2353, 3585, 5185, 6721, 7201, 8380, 8911, 8961, 11521, 11782, 12673, 12801, 17101, 18241, 20737, 25201, 26625, 26677, 26937, 29697, 29953, 30721, 30889, 32896

Offset: 1

Author

Labos Elemer, Oct 18 2001

Keywords

• nonn

Examples

			m=136, phi(136)=64, sigma(136)=270, product=17280, quotient=128; for primes the formula holds.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A000010, A000203, A062354, A011257.

Programs

GAP

Filtered([2..40000],m->Phi(m)*Sigma(m) mod (m-1)=0 and not IsPrime(m)); # Muniru A Asiru, Jun 18 2018

Maple

with(numtheory): select(m->modp(phi(m)*sigma(m),m-1)=0 and not isprime(m),[$2..40000]); # Muniru A Asiru, Jun 18 2018

Mathematica

Do[s=EulerPhi[n]*DivisorSigma[1, n]; If[IntegerQ[s/(n-1)]&&!PrimeQ[n], Print[n]], {n, 1, 100000}]

PARI

{ n=0; for (m=2, 10^9, s=eulerphi(m)*sigma(m); if (s%(m-1) == 0 && !isprime(m), write("b065149.txt", n++, " ", m); if (n==500, return)) ) } \\ Harry J. Smith, Oct 12 2009

Formula

(A000010(m)*A000203(m)) mod (m-1) = 0, m is composite.

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Oct 12 2009