

A066175


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


4



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

1,2


COMMENTS

If n=2^k1, where either k=1, or n is a Mersenne prime (A000668), or sigma(n)=3*2^(k1), 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^k1, where either k=1, or n is a Mersenne prime (A000668), or sigma(n)=3*2^(k1), then A000217(n) divides sigma(A000217(n)).  Altug Alkan, Jul 25 2016


LINKS



EXAMPLE

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


MATHEMATICA

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


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS

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


STATUS

approved



