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A371531 a(n) is the multiplicative order of A053669(n) modulo n.

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%I A371531 #27 Apr 25 2024 13:58:50
%S A371531 1,1,2,2,4,2,3,2,6,4,10,2,12,6,4,4,8,6,18,4,6,5,11,2,20,3,18,6,28,4,5,
%T A371531 8,10,16,12,6,36,18,12,4,20,6,14,10,12,11,23,4,21,20,8,6,52,18,20,6,
%U A371531 18,28,58,4,60,30,6,16,12,10,66,16,22,12,35,6,9,18,20
%N A371531 a(n) is the multiplicative order of A053669(n) modulo n.
%F A371531 a(2k+1) = A002326(k) for k >= 1.
%F A371531 a(2k) = ord(A284723(k), 2k).
%t A371531 a[n_] := Module[{p = 2}, While[Divisible[n, p], p = NextPrime[p]]; MultiplicativeOrder[p, n]]; Array[a, 75] (* _Amiram Eldar_, Mar 26 2024 *)
%o A371531 (Python)
%o A371531 from sympy.ntheory.residue_ntheory import n_order
%o A371531 from sympy import nextprime
%o A371531 def a(n):
%o A371531   if n == 1: return 1
%o A371531   if n & 1 == 1: return n_order(2, n)
%o A371531   p = 2
%o A371531   while n % p == 0:
%o A371531     p = nextprime(p)
%o A371531   return n_order(p, n)
%o A371531 print([a(n) for n in range(1, 76)])
%o A371531 (PARI) f(n) = forprime(p=2, , if(n%p, return(p))); \\ A053669
%o A371531 a(n) = znorder(Mod(f(n), n)); \\ _Michel Marcus_, Mar 26 2024
%Y A371531 Cf. A002326, A053669, A284723.
%K A371531 nonn
%O A371531 1,3
%A A371531 _DarĂ­o Clavijo_, Mar 26 2024