A336644 a(n) = (n-rad(n)) / core(n), where rad(n) and core(n) give the squarefree kernel and squarefree part of n, respectively.

0, 0, 0, 2, 0, 0, 0, 3, 6, 0, 0, 2, 0, 0, 0, 14, 0, 6, 0, 2, 0, 0, 0, 3, 20, 0, 8, 2, 0, 0, 0, 15, 0, 0, 0, 30, 0, 0, 0, 3, 0, 0, 0, 2, 6, 0, 0, 14, 42, 20, 0, 2, 0, 8, 0, 3, 0, 0, 0, 2, 0, 0, 6, 62, 0, 0, 0, 2, 0, 0, 0, 33, 0, 0, 20, 2, 0, 0, 0, 14, 78, 0, 0, 2, 0, 0, 0, 3, 0, 6, 0, 2, 0, 0, 0, 15, 0, 42, 6, 90, 0, 0, 0, 3, 0

Offset: 1

Author

Antti Karttunen, Jul 28 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A007913, A007947, A008833, A066503, A336642, A336643.

Programs

PARI

A336644(n) = ((n-factorback(factorint(n)[, 1])) / core(n));

Python

from math import prod
from sympy.ntheory.factor_ import primefactors, core
def A336644(n): return (n-prod(primefactors(n)))//core(n) # Chai Wah Wu, Dec 30 2021

Formula

a(n) = A066503(n) / A007913(n) = (n-A007947(n)) / A007913(n).

a(n) = A008833(n) - A336643(n).