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A138227 Odd positive integers n for which A137576((n-1)/2)-1 is not a multiple of A000010(n). 6
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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 A301789 A244166

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

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Last modified June 1 02:09 EDT 2020. Contains 334758 sequences. (Running on oeis4.)