A368540 The smallest unitary divisor d of n such that n/d is a term of A138302.

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, 64, 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, 1, 1, 1, 1, 1, 32, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 27, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 125, 1, 1

Offset

1,8

Comments

First differs from A368167 at n = 64 and from A367513 at n = 128.

Links

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

Formula

a(n) = n / A367168(n).

Multiplicative with a(p^e) = p^(e-A048298(e)).

a(n) >= 1, with equality if and only if n is in A138302.

Mathematica

f[p_, e_] := If[e == 2^IntegerExponent[e, 2], 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 << valuation(f[i, 2], 2), 1, f[i, 1]^f[i, 2])); }
(Python)
from math import prod
from sympy import factorint
def A368540(n): return prod(p**e for p, e in factorint(n).items() if not e or (e&-e)^e) # Chai Wah Wu, Dec 30 2023

Crossrefs

Cf. A048298, A077610, A138302, A367168, A367513, A368167.

Sequence in context: A056191 A368167 A367513 * A103760 A268355 A008834

Adjacent sequences: A368537 A368538 A368539 * A368541 A368542 A368543

Keyword

nonn,easy,mult

Author

Amiram Eldar, Dec 29 2023

Status

approved