cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A366906 The largest exponentially evil divisor of n.

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%I A366906 #7 Oct 28 2023 03:48:35
%S A366906 1,1,1,1,1,1,1,8,1,1,1,1,1,1,1,8,1,1,1,1,1,1,1,8,1,1,27,1,1,1,1,32,1,
%T A366906 1,1,1,1,1,1,8,1,1,1,1,1,1,1,8,1,1,1,1,1,27,1,8,1,1,1,1,1,1,1,64,1,1,
%U A366906 1,1,1,1,1,8,1,1,1,1,1,1,1,8,27,1,1,1,1,1
%N A366906 The largest exponentially evil divisor of n.
%C A366906 The largest divisor of n that is an exponentially evil number (A262675).
%C A366906 The number of exponentially evil divisors of n is A366902(n) and their sum is A366904(n).
%H A366906 Amiram Eldar, <a href="/A366906/b366906.txt">Table of n, a(n) for n = 1..10000</a>
%F A366906 Multiplicative with a(p^e) = p^max{k=1..e, k evil}.
%F A366906 a(n) <= n, with equality if and only if n is exponentially evil number (A262675).
%F A366906 a(n) >= 1, with equality if and only if n is a cubefree number (A004709).
%t A366906 maxEvil[e_] := Module[{k = e}, While[OddQ[DigitCount[k, 2, 1]], k--]; k]; f[p_, e_] := p^maxEvil[e]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A366906 (PARI) s(n) = {my(k = n); while(hammingweight(k)%2, k--); k;}
%o A366906 a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^s(f[i, 2]));}
%Y A366906 Cf. A004709, A262675, A366902, A366904.
%Y A366906 Similar sequences: A353897, A365683, A366905.
%K A366906 nonn,easy,mult
%O A366906 1,8
%A A366906 _Amiram Eldar_, Oct 27 2023