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

1,2

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

Cf. A137576, A000010, A002326, A006694.

Sequence in context: A288452 A338316 A193414 * A074775 A356845 A225105

Adjacent sequences: A138214 A138215 A138216 * A138218 A138219 A138220

Keyword

nonn

Author

Vladimir Shevelev, May 05 2008

Extensions

Extended by Ray Chandler, May 08 2008

Status

approved