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a(n) = log_2(A372468(n)).
3

%I #7 May 02 2024 10:06:31

%S 0,1,1,1,2,1,2,2,1,1,2,2,1,1,2,2,1,3,2,2,1,3,1,2,2,2,1,2,2,3,1,3,1,2,

%T 1,2,1,3,2,3,2,2,1,1,2,2,3,1,2,3,1,1,2,2,3,1,2,1,2,2,2,3,1,2,2,2,2,1,

%U 1,3,1,3,3,2,1,1,3,2,1,3,2,2,2,4,2,2,2

%N a(n) = log_2(A372468(n)).

%H Amiram Eldar, <a href="/A372469/b372469.txt">Table of n, a(n) for n = 1..10000</a>

%t f[n_] := Module[{p = Times @@ (1 + FactorInteger[n][[;; , 2]]), e}, e = IntegerExponent[p, 2]; If[p == 2^e, e, Nothing]]; f[1] = 0; Array[f, 150]

%o (PARI) lista(kmax) = {my(p, e); for(k = 1, kmax, p = vecprod(apply(x -> x + 1, factor(k)[, 2])); e = valuation(p, 2); if(p >> e == 1, print1(e, ", "))); }

%Y Cf. A372468.

%K nonn,easy

%O 1,5

%A _Amiram Eldar_, May 02 2024