OFFSET
1,1
COMMENTS
Theorem: If m is in the sequence, sigma(m) is an odd number, 2^n-1 is a prime greater than 3 (a Mersenne prime) and gcd(m, 2^n-1)=1, then m*(2^n-1) is in the sequence (the proof is easy). One of the results of this theorem is: If p=2^n-1 is a prime greater than 3 then 36*p, 288*p, 115200*p and 4147200*p are in the sequence. - Farideh Firoozbakht, Jul 08 2006
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..45 (terms < 10^11)
MATHEMATICA
uphi[n_] := (A = FactorInteger[n]; l = Length[A]; Product[A[[k]][[1]] ^A[[k]][[2]] - 1, {k, l}]); Do[If[uphi[DivisorSigma[1, n]] == 2n, Print[n]], {n, 70000000}] (* Farideh Firoozbakht, Jul 08 2006 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Corrected and extended by Farideh Firoozbakht, Jul 08 2006
STATUS
approved