A070037 Nonprime numbers k such that sigma(k) == k+1 (mod phi(k)).

1, 4, 15, 900, 903, 28611063

Offset: 1

Author

Labos Elemer, Apr 18 2002

Keywords

• more
• nonn

Comments

Nonprime numbers k such that Chowla(k)/phi(k) is an integer.

a(7) > 3.7*10^12. - Giovanni Resta, Jul 14 2013

3^30*13*852977547249259 and 3^36*13*621820631944710643 are also terms. - Giovanni Resta, Nov 14 2019

Examples

			Below 30000000 only 5 composite numbers were found: C = {4,15,900,902,28611063}, Chowla(C) = {2,8,1920,504,17600976}, phi(C) = {2,8,240,504,17600976}, quotient = {1,1,8,1,1}.
		

Crossrefs

Cf. A000010, A000203, A048050.

Programs

Mathematica

s2[x_] := DivisorSigma[1, x]-x-1 e0[x_] := EulerPhi[x] Do[s=s2[n]/e0[n]; If[IntegerQ[s]&&!PrimeQ[n], Print[{n, s2[n], e0[n], s}]], {n, 1, 1000000}]

PARI

is(n)=!isprime(n) && Mod(sigma(n),eulerphi(n))==n+1 \\ Charles R Greathouse IV, Jun 06 2013