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A384231 Index of the largest odd noncomposite divisor in the list of divisors of n.

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%I A384231 #14 Jun 03 2025 00:59:39
%S A384231 1,1,2,1,2,3,2,1,2,3,2,3,2,3,3,1,2,3,2,4,3,3,2,3,2,3,2,4,2,4,2,1,3,3,
%T A384231 3,3,2,3,3,4,2,5,2,4,3,3,2,3,2,3,3,4,2,3,3,4,3,3,2,5,2,3,3,1,3,5,2,4,
%U A384231 3,4,2,3,2,3,3,4,3,5,2,4,2,3,2,6,3,3,3,5,2,4,3,4,3,3,3,3,2,3,4,4
%N A384231 Index of the largest odd noncomposite divisor in the list of divisors of n.
%C A384231 a(n) = 1 if and only if n is a power of 2.
%e A384231 For n = 30 the divisors of 30 are [1, 2, 3, 5, 6, 10, 15, 30] and the largest odd noncomposite divisor is 5 and 5 is its 4th divisor, so a(30) = 4.
%t A384231 a[n_] := Module[{m = n/2^IntegerExponent[n, 2]}, If[m == 1, 1, Position[Divisors[n], FactorInteger[m][[-1, 1]]][[1, 1]]]]; Array[a, 100] (* _Amiram Eldar_, May 29 2025 *)
%Y A384231 Companion of A383401.
%Y A384231 Right border of A384234.
%Y A384231 Cf. A006005 (odd noncomposite numbers).
%Y A384231 Cf. A000079, A027750, A384232, A384233.
%K A384231 nonn,easy
%O A384231 1,3
%A A384231 _Omar E. Pol_, May 29 2025