A066175 Numbers k such that sigma(phi(sigma(k))) = k.

1, 3, 7, 15, 31, 127, 1023, 8191, 131071, 524287, 2147483647

Offset: 1

Author

Joseph L. Pe, Dec 15 2001

Keywords

• nonn
• more

Comments

If n=2^k-1, where either k=1, or n is a Mersenne prime (A000668), or sigma(n)=3*2^(k-1), then n is in the sequence; are there any terms not of these forms? The last form includes the terms 15 and 1023; are there others like this?

Is this sequence infinite?

It is conjectured that there are infinitely many Mersenne primes. So this conjecture also supports that this sequence is infinite. Additionally, if n=2^k-1, where either k=1, or n is a Mersenne prime (A000668), or sigma(n)=3*2^(k-1), then A000217(n) divides sigma(A000217(n)). - Altug Alkan, Jul 25 2016

Examples

			sigma(phi(sigma(31))) = sigma(phi(32)) = sigma(16) = 31.
		

Crossrefs

Cf. A000217, A000668.

Programs

Mathematica

Select[Range[1, 10^6], DivisorSigma[1, EulerPhi[DivisorSigma[1, # ]]]==#&]

Extensions

Edited by Dean Hickerson, Feb 20 2002

a(11) from Jud McCranie, Jun 23 2005; no more terms < 4000000000.