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A367934 a(n) is the smallest multiple of n that is an exponentially evil number (A262675).

%I A367934 #8 Dec 05 2023 08:56:14
%S A367934 1,8,27,8,125,216,343,8,27,1000,1331,216,2197,2744,3375,32,4913,216,
%T A367934 6859,1000,9261,10648,12167,216,125,17576,27,2744,24389,27000,29791,
%U A367934 32,35937,39304,42875,216,50653,54872,59319,1000,68921,74088,79507,10648,3375,97336
%N A367934 a(n) is the smallest multiple of n that is an exponentially evil number (A262675).
%C A367934 First differs from A356192 at n = 64.
%H A367934 Amiram Eldar, <a href="/A367934/b367934.txt">Table of n, a(n) for n = 1..10000</a>
%F A367934 Multiplicative with a(p^e) = p^s(e), s(e) = min{k >= e, k is evil}.
%F A367934 a(n) = n * A367932(n).
%F A367934 a(n) >= n, with equality if and only if n is an exponentially evil number (A262675).
%F A367934 Sum_{k=1..n} a(k) ~  c * n^4 / 4, where c = Product_{p prime} f(1/p) = 0.623746285..., where f(x) = (1-x) * (1 + Sum_{k>=1} x^(4*k-s(k))), and s(k) is defined above.
%F A367934 Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + Sum_{k>=1} 1/p^s(k)) = 1.70170328791367919805... .
%t A367934 f[p_, e_] := Module[{k = e}, While[! EvenQ[DigitCount[k, 2 ,1]], k++]; p^k]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A367934 (PARI) s(e) = {my(k = e); while(hammingweight(k)%2, k++); k; };
%o A367934 a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^s(f[i, 2])); }
%Y A367934 Cf. A262675, A367932.
%Y A367934 Similar sequences: A356192, A365684, A367933.
%K A367934 nonn,easy,mult,base
%O A367934 1,2
%A A367934 _Amiram Eldar_, Dec 05 2023