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%I #8 Dec 05 2023 08:55:40
%S 1,4,9,2,25,36,49,1,3,100,121,18,169,196,225,2,289,12,361,50,441,484,
%T 529,9,5,676,1,98,841,900,961,1,1089,1156,1225,6,1369,1444,1521,25,
%U 1681,1764,1849,242,75,2116,2209,18,7,20,2601,338,2809,4,3025,49,3249,3364
%N a(n) is the smallest number k such that k*n is an exponentially evil number (A262675).
%C First differs from A365298 at n = 64.
%H Amiram Eldar, <a href="/A367932/b367932.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = p^s(e), s(e) = min{k >= e, k is evil} - e.
%F a(n) = A367934(n)/n.
%F a(n) >= 1, with equality if and only if n is an exponentially evil number (A262675).
%F Sum_{k=1..n} a(k) ~ c * n^3 / 3, where c = Product_{p prime} f(1/p) = 0.623746285..., where f(x) = (1-x) * (1 + Sum_{k>=1} (x^(3*k-s(k))), and s(k) is defined above.
%t f[p_, e_] := Module[{k = e}, While[! EvenQ[DigitCount[k, 2 ,1]], k++]; p^(k-e)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o (PARI) s(e) = {my(k = e); while(hammingweight(k)%2, k++); k - e; };
%o a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^s(f[i, 2])); }
%Y Cf. A001969, A262675, A367934.
%Y Similar sequences: A365298, A365685, A367931.
%K nonn,easy,mult,base
%O 1,2
%A _Amiram Eldar_, Dec 05 2023
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