A138217 Odd numbers n for which A137576((n-1)/2)-1 is a multiple of A000010(n).

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25, 27, 29, 31, 33, 37, 39, 41, 43, 47, 49, 53, 55, 57, 59, 61, 63, 67, 71, 73, 79, 81, 83, 87, 89, 95, 97, 101, 103, 107, 109, 111, 113, 119, 121, 125, 127, 131, 135, 137, 139, 143, 149, 151, 153, 157, 159, 161, 163, 167, 169, 173

Offset: 1

Author

Vladimir Shevelev, May 05 2008

Keywords

• nonn

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

Crossrefs

Cf. A137576, A000010, A002326, A006694.

Programs

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 *)

Extensions

Extended by Ray Chandler, May 08 2008