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A066175 Numbers k such that sigma(phi(sigma(k))) = k. 4
1, 3, 7, 15, 31, 127, 1023, 8191, 131071, 524287, 2147483647 (list; graph; refs; listen; history; text; internal format)
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
EXAMPLE
sigma(phi(sigma(31))) = sigma(phi(32)) = sigma(16) = 31.
MATHEMATICA
Select[Range[1, 10^6], DivisorSigma[1, EulerPhi[DivisorSigma[1, # ]]]==#&]
CROSSREFS
Sequence in context: A147285 A147250 A336701 * A132978 A336976 A117079
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

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Last modified June 9 00:56 EDT 2023. Contains 363165 sequences. (Running on oeis4.)