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A366906
The largest exponentially evil divisor of n.
7
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, 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, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 8, 27, 1, 1, 1, 1, 1
OFFSET
1,8
COMMENTS
The largest divisor of n that is an exponentially evil number (A262675).
The number of exponentially evil divisors of n is A366902(n) and their sum is A366904(n).
LINKS
FORMULA
Multiplicative with a(p^e) = p^max{k=1..e, k evil}.
a(n) <= n, with equality if and only if n is exponentially evil number (A262675).
a(n) >= 1, with equality if and only if n is a cubefree number (A004709).
MATHEMATICA
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]
PROG
(PARI) s(n) = {my(k = n); while(hammingweight(k)%2, k--); k; }
a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^s(f[i, 2])); }
CROSSREFS
Similar sequences: A353897, A365683, A366905.
Sequence in context: A268355 A008834 A368170 * A056201 A368329 A360540
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Oct 27 2023
STATUS
approved