A366906 The largest exponentially evil divisor of n.

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A004709, A262675, A366902, A366904.

Similar sequences: A353897, A365683, A366905.

Sequence in context: A268355 A008834 A368170 * A056201 A368329 A360540

Adjacent sequences: A366903 A366904 A366905 * A366907 A366908 A366909

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 27 2023

Status

approved