A368170 The largest cubefull exponentially odd 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, 32, 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

First differs from A008834 at n = 32, and from A366906 at n = 64.

Links

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

Formula

Multiplicative with a(p^e) = 1 if e <= 2, a(p^e) = p^e if e is odd and e > 1, and p^(e-1) otherwise.

a(n) = n/A368171(n).

a(n) >= 1, with equality if and only if n is cubefree (A004709).

a(n) <= n, with equality if and only if n is in A335988.

Mathematica

f[p_, e_] := If[e <= 2, 1, If[EvenQ[e], p^(e-1), p^e]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = {my(f=factor(n)); prod(i=1, #f~, if(f[i, 2] <= 2, 1, if(!(f[i, 2]%2), f[i, 1]^(f[i, 2]-1), f[i, 1]^f[i, 2])))};

Crossrefs

Cf. A004709, A335988, A350390, A356192, A368167, A368171.

Cf. A008834, A366906.

Sequence in context: A103760 A268355 A008834 * A366906 A056201 A368329

Adjacent sequences: A368167 A368168 A368169 * A368171 A368172 A368173

Keyword

nonn,easy,mult

Author

Amiram Eldar, Dec 14 2023

Status

approved