OFFSET
1,1
COMMENTS
If p = 2^k + 3 and both numbers p & q = (1/2)*(p^2 - 3p - 2) are primes then q is in the sequence, because sigma(sigma(q)) = sigma(q+1) = sigma((1/2)*(p-3)*p) = sigma(2^(n-1)*p) = (2^n-1)*(p+1) = (p-4)*(p+1) = p^2 - 3p - 4 = 2q - 2 = 2*phi(q). 13, 43, 151 & 2143 are such terms corresponding to n = 2, 3, 4 & 6.
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..54 (terms < 10^10)
EXAMPLE
sigma(sigma(36300841)) = sigma(36313684) = 72576000 = 2*36288000 = 2*phi(36300841) so 36300841 is in the sequence.
MATHEMATICA
lst = {}; fQ[n_] := DivisorSigma[1, DivisorSigma[1, n]] == 2 EulerPhi@n; Do[ If[ fQ@n, AppendTo[lst, n]; Print@n], {n, 252000000}] (* Robert G. Wilson v, Jan 01 2008 *)
PROG
(PARI) is(n) = sigma(sigma(n))==2*eulerphi(n) \\ Felix Fröhlich, May 18 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Farideh Firoozbakht, Dec 30 2007
EXTENSIONS
More terms from Robert G. Wilson v, Jan 01 2008
STATUS
approved