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

Author

Jianing Song, Feb 13 2019

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A001567, A002326, A300101, A306413.

Programs

Mathematica

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

PARI

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

Formula

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

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