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A306413 a(n) is the multiplicative order of 2 modulo A001567(n). 1
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 (list; graph; refs; listen; history; text; internal format)
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 A002997.

LINKS

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

FORMULA

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

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.

Sequence in context: A267626 A189947 A197705 * A187205 A104045 A102546

Adjacent sequences:  A306410 A306411 A306412 * A306414 A306415 A306416

KEYWORD

nonn

AUTHOR

Jianing Song, Feb 13 2019

STATUS

approved

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Last modified September 25 02:25 EDT 2021. Contains 347651 sequences. (Running on oeis4.)