A326186 a(n) = n - A057521(n), where A057521 gives the powerful part of n.

0, 1, 2, 0, 4, 5, 6, 0, 0, 9, 10, 8, 12, 13, 14, 0, 16, 9, 18, 16, 20, 21, 22, 16, 0, 25, 0, 24, 28, 29, 30, 0, 32, 33, 34, 0, 36, 37, 38, 32, 40, 41, 42, 40, 36, 45, 46, 32, 0, 25, 50, 48, 52, 27, 54, 48, 56, 57, 58, 56, 60, 61, 54, 0, 64, 65, 66, 64, 68, 69, 70, 0, 72, 73, 50, 72, 76, 77, 78, 64, 0, 81, 82, 80, 84

Offset: 1

Author

Antti Karttunen, Jul 11 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A057521, A326185.

Cf. also A010848.

Programs

PARI

A057521(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 2]>1, f[i, 1]^f[i, 2], 1)); }; \\ From A057521.
A326186(n) = (n-A057521(n));

Python

from math import prod
from sympy import factorint
def A326186(n): return n-n//prod(p for p, e in factorint(n).items() if e == 1) # Chai Wah Wu, Nov 14 2022

Formula

a(n) = n - A057521(n).