A138227 Odd positive integers n for which A137576((n-1)/2)-1 is not a multiple of A000010(n).

21, 35, 45, 51, 65, 69, 75, 77, 85, 91, 93, 99, 105, 115, 117, 123, 129, 133, 141, 145, 147, 155, 165, 171, 185, 187, 189, 195, 203, 205, 213, 215, 217, 219, 221, 231, 235, 237, 245, 247, 253, 255, 259, 261, 265, 267, 273, 275, 279, 285, 291, 299, 301, 305

Offset: 1

Author

Vladimir Shevelev, May 05 2008

Keywords

• nonn

Comments

All terms are composite numbers since if p is an odd prime then A137576((p-1)/2)-1=p-1=A000010(p).

Conjecture. This sequence is infinite.

Links

• Ray Chandler, Table of n, a(n) for n = 1..6500

Crossrefs

Cf. A137576, A000010, A002326, A006694.

Programs

Mathematica

A137576[n_] := With[{t = MultiplicativeOrder[2, 2 n + 1]}, t*DivisorSum[2 n + 1, EulerPhi[#]/MultiplicativeOrder[2, #] &] - t + 1]; Select[Range[1, 1000, 2], !Divisible[A137576[(# - 1)/2] - 1, EulerPhi[#]]&] (* Jean-François Alcover, Dec 07 2015 *)

PARI

is(n)=my(t); n%2 && (sumdiv(n,d,eulerphi(d)/(t=znorder(Mod(2, d))))*t-t)%eulerphi(n)>0 \\ Charles R Greathouse IV, Feb 20 2013

Extensions

Extended by Ray Chandler, May 08 2008