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

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

Offset

1,2

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

Links

Table of n, a(n) for n=1..11.

Example

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

Mathematica

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

Crossrefs

Cf. A000217, A000668.

Sequence in context: A147285 A147250 A336701 * A132978 A336976 A368346

Adjacent sequences: A066172 A066173 A066174 * A066176 A066177 A066178

Keyword

nonn,more

Author

Joseph L. Pe, Dec 15 2001

Extensions

Edited by Dean Hickerson, Feb 20 2002

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

Status

approved