OFFSET
1,2
COMMENTS
The sequence contains all odd primes. Indeed, if p is a prime then A137576((p-1)/2)-1=p-1=A000010(p).
Conjecture: the sequence contains infinitely many composite numbers.
The conjecture is true because of the sequence contains all powers of odd primes. Indeed, A137576((P^k-1)/2)-1=k*A000010(p^k). - Vladimir Shevelev, May 29 2008
LINKS
Ray Chandler, Table of n, a(n) for n=1..3501
MATHEMATICA
A137576[n_] := Module[{t}, (t = MultiplicativeOrder[2, 2 n + 1])* DivisorSum[2 n + 1, EulerPhi[#]/MultiplicativeOrder[2, #] &] - t + 1];
okQ[n_] := OddQ[n] && Divisible[A137576[(n - 1)/2] - 1, EulerPhi[n]];
Reap[For[k = 1, k < 200, k += 2, If[okQ[k], Sow[k]]]][[2, 1]] (* Jean-François Alcover, Jan 11 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, May 05 2008
EXTENSIONS
Extended by Ray Chandler, May 08 2008
STATUS
approved