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

1,1

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

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 *)

Prog

(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

Crossrefs

Cf. A137576, A000010, A002326, A006694.

Sequence in context: A330949 A248020 A290435 * A246157 A364029 A301789

Adjacent sequences: A138224 A138225 A138226 * A138228 A138229 A138230

Keyword

nonn

Author

Vladimir Shevelev, May 05 2008

Extensions

Extended by Ray Chandler, May 08 2008

Status

approved