A368167 The largest unitary divisor of n that is a cubefull exponentially odd number (A335988).

1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 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, 1, 1, 1, 1, 1, 1, 27, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1,8

Comments

First differs from A056191 and A366126 at n = 32, and from A367513 at n = 64.

Also, the largest exponentially odd unitary divisor of the powerful part on n.

Also, the powerful part of the largest exponentially odd unitary divisor of n.

Links

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

Formula

Multiplicative with a(p^e) = p^e if e is odd that is larger than 1, and 1 otherwise.

a(n) = A350389(A057521(n)).

a(n) = A057521(A350389(n)).

a(n) >= 1, with equality if and only if n is in A335275.

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

Mathematica

f[p_, e_] := If[e == 1 || EvenQ[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] == 1 || !(f[i, 2]%2), 1, f[i, 1]^f[i, 2])); }

Crossrefs

Cf. A057521, A077610, A335275, A335988, A350389, A368168, A368169.

Cf. A056191, A366126, A367513.

Sequence in context: A199461 A366126 A056191 * A367513 A368540 A103760

Adjacent sequences: A368164 A368165 A368166 * A368168 A368169 A368170

Keyword

nonn,easy,mult

Author

Amiram Eldar, Dec 14 2023

Status

approved