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

%I A306413 #22 Nov 10 2023 09:23:42
%S A306413 10,40,28,24,18,36,28,11,56,36,60,28,36,16,230,15,14,660,36,52,80,198,
%T A306413 30,252,72,200,60,58,20,42,22,45,48,28,96,70,40,48,460,180,60,3432,88,
%U A306413 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
%N A306413 a(n) is the multiplicative order of 2 modulo A001567(n).
%C A306413 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.
%H A306413 Amiram Eldar, <a href="/A306413/b306413.txt">Table of n, a(n) for n = 1..10000</a>
%F A306413 a(n) = A002326((A001567(n)-1)/2).
%F A306413 a(n) = (A001567(n) - 1) / A300101(n). - _Jianing Song_, Dec 12 2021
%e A306413 A001567(1) = 341, 341 divides 2^10 - 1, 341 = 34*10 + 1.
%e A306413 A001567(2) = 561, 561 divides 2^40 - 1, 561 = 14*40 + 1.
%e A306413 A001567(3) = 645, 645 divides 2^28 - 1, 645 = 23*28 + 1.
%e A306413 A001567(4) = 1105, 1105 divides 2^24 - 1, 1105 = 46*24 + 1.
%t A306413 MultiplicativeOrder[2, #] & /@ Select[Range[1, 10^5, 2], CompositeQ[#] && PowerMod[2, # - 1, #] == 1 &] (* _Amiram Eldar_, Jun 29 2019 *)
%o A306413 (PARI) forstep(n=3, 1e5, 2, my(m=znorder(Mod(2,n))); if((n-1)%m==0 && !isprime(n), print1(m, ", ")))
%Y A306413 Cf. A001567, A002326, A300101, A306413.
%K A306413 nonn
%O A306413 1,1
%A A306413 _Jianing Song_, Feb 13 2019