OFFSET
1,1
COMMENTS
If p = 3*2^(m-1)-1 is an odd prime then 2^m*p is in the sequence because phi(2^m*p) = 2^(m-1)*(3*2^(m-1)-2), sigma(2^m*p) = (2^(m+1)-1)*(3*2^(m-1)) so phi(2^m*p)+sigma(2^m*p) = 2^(m-1)*(3* 2^(m-1)-2)+(2^(m+1)-1)*(3*2^(m-1)) = 3*2^(2m-2)-2^m+3*2^(2m)-3*2^ (m-1) = 2^(m-1)*(3*2^(m-1)-2+3*2^(m+1)-3) = 2^(m-1)*(3*5*2^(m-1)-5) = 5/2*2^m*(3*2^(m-1)-1) = 5/2*(2^m*p). Except 18 & 5238976 all known terms of the sequence are of the form 2^m*(3*2^(m-1)-1), where (3*2^(m-1)-1) is prime.
a(15) > 10^13. - Giovanni Resta, Jul 13 2015
EXAMPLE
25161728 is in the sequence because phi(25161728) + sigma(25161728) = 12578816 + 50325504 = 5/2*25161728.
MATHEMATICA
Do[If[DivisorSigma[1, n]+EulerPhi[n]==5/2*n, Print[n]], {n, 200000000}]
PROG
(PARI) isok(n) = eulerphi(n) + sigma(n) == 5*n/2; \\ Michel Marcus, Jul 14 2015
CROSSREFS
KEYWORD
more,nonn
AUTHOR
Farideh Firoozbakht, Feb 12 2006
EXTENSIONS
a(10)-a(12) from Donovan Johnson, Feb 29 2012
a(13) from Donovan Johnson, Apr 04 2012
a(14) from Giovanni Resta, Jul 13 2015
STATUS
approved