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A274720 Odd numbers n such that n is not coprime to the multiplicative order of 2 mod n. 2
9, 21, 25, 27, 39, 45, 49, 55, 57, 63, 75, 81, 99, 105, 111, 117, 121, 125, 135, 147, 153, 155, 165, 169, 171, 175, 183, 189, 195, 201, 203, 205, 207, 219, 225, 231, 237, 243, 245, 253, 261, 273, 275, 279, 285, 289, 291, 297, 301, 305, 309, 315, 325, 327 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Odd numbers n such that gcd(n, A002326((n-1)/2)) > 1.

A prime power p^k is in the sequence unless 2^(p-1) == 1 (mod p^k). In particular, for p^2 to not be in the sequence p must be a Wieferich prime.

If n is in the sequence, then so is every odd multiple of n.

All odd multiples of members of A273202. - Robert Israel, Jul 28 2016

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

25 is in the sequence because the order of 2 mod 25 is 20 and gcd(20,25)=5>1.

MAPLE

remove(t -> igcd(t, numtheory:-order(2, t))=1, [seq(i, i=3..1000, 2)]);

MATHEMATICA

A274720Q = OddQ[#] && ! CoprimeQ[MultiplicativeOrder[2, #], #] &; Select[Range[200], A274720Q] (* JungHwan Min, Jul 29 2016 *)

PROG

(PARI) is(n) = n%2!=0 && gcd(n, znorder(Mod(2, n))) > 1 \\ Felix Fröhlich, Jul 27 2016

CROSSREFS

Subset of A139392.

Cf. A001220, A002326, A273202.

Sequence in context: A138786 A305733 A139392 * A338318 A322336 A327685

Adjacent sequences:  A274717 A274718 A274719 * A274721 A274722 A274723

KEYWORD

nonn

AUTHOR

Robert Israel, Jul 27 2016

STATUS

approved

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Last modified May 18 19:51 EDT 2022. Contains 353824 sequences. (Running on oeis4.)