A065148 Nonprimes m such that phi(m)*sigma(m) is divisible by m+1.

15, 20, 35, 95, 104, 143, 207, 255, 287, 319, 323, 464, 539, 650, 890, 899, 1023, 1034, 1199, 1295, 1349, 1407, 1519, 1763, 1952, 2015, 2204, 2834, 2975, 3599, 4031, 4454, 4607, 5183, 6479, 9215, 9503, 9799, 10403, 11339, 11663, 12095, 12824, 13055

Offset: 1

Author

Labos Elemer, Oct 18 2001

Keywords

• nonn

Comments

Every prime p satisfies A000010(p)*A000203(p) == 0 (mod p+1).

Examples

			m = 95 is a term since phi(95) = 72, sigma(95) = 120, product = 8640, product/(m+1) = 90.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..5000 (terms 1..500 from Harry J. Smith)

Crossrefs

Cf. A000010, A000203, A062354, A011257.

Programs

Mathematica

Do[s=EulerPhi[n]*DivisorSigma[1, n]; If[IntegerQ[s/(n+1)]&&!PrimeQ[n], Print[n]], {n, 1, 100000}]
Select[Range[14000],!PrimeQ[#]&&Divisible[EulerPhi[#]DivisorSigma[1,#],#+1]&] (* Harvey P. Dale, Jul 08 2017 *)

PARI

{ n=0; for (m=1, 10^9, s=eulerphi(m)*sigma(m); if (s%(m+1) == 0 && !isprime(m), write("b065148.txt", n++, " ", m); if (n==500, return)) ) } \\ Harry J. Smith, Oct 12 2009

Formula

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

Extensions

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

Definition clarified by Harvey P. Dale, Jul 08 2017