A306413 a(n) is the multiplicative order of 2 modulo A001567(n).

10, 40, 28, 24, 18, 36, 28, 11, 56, 36, 60, 28, 36, 16, 230, 15, 14, 660, 36, 52, 80, 198, 30, 252, 72, 200, 60, 58, 20, 42, 22, 45, 48, 28, 96, 70, 40, 48, 460, 180, 60, 3432, 88, 72, 102, 112, 168, 44, 264, 60, 192, 21, 144, 156, 30, 153, 28, 180, 100, 22, 1012, 36, 58, 48, 60, 28, 612, 120, 60, 166, 1008, 52, 532, 148, 9840

Offset

1,1

Comments

By definition, A001567 lists the odd composite numbers k such that ord(2,k) divides k - 1, where ord(2,k) is the multiplicative order of 2 modulo k. This sequence lists the values for ord(2,k) when k runs through A001567.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A002326((A001567(n)-1)/2).

a(n) = (A001567(n) - 1) / A300101(n). - Jianing Song, Dec 12 2021

Example

A001567(1) = 341, 341 divides 2^10 - 1, 341 = 34*10 + 1.
A001567(2) = 561, 561 divides 2^40 - 1, 561 = 14*40 + 1.
A001567(3) = 645, 645 divides 2^28 - 1, 645 = 23*28 + 1.
A001567(4) = 1105, 1105 divides 2^24 - 1, 1105 = 46*24 + 1.

Mathematica

MultiplicativeOrder[2, #] & /@ Select[Range[1, 10^5, 2], CompositeQ[#] && PowerMod[2, # - 1, #] == 1 &] (* Amiram Eldar, Jun 29 2019 *)

Prog

(PARI) forstep(n=3, 1e5, 2, my(m=znorder(Mod(2, n))); if((n-1)%m==0 && !isprime(n), print1(m, ", ")))

Crossrefs

Cf. A001567, A002326, A300101, A306413.

Sequence in context: A189947 A370792 A197705 * A187205 A104045 A102546

Adjacent sequences: A306410 A306411 A306412 * A306414 A306415 A306416

Keyword

nonn

Author

Jianing Song, Feb 13 2019

Status

approved