A336158 The least number with the prime signature of the odd part of n: a(n) = A046523(A000265(n)).

1, 1, 2, 1, 2, 2, 2, 1, 4, 2, 2, 2, 2, 2, 6, 1, 2, 4, 2, 2, 6, 2, 2, 2, 4, 2, 8, 2, 2, 6, 2, 1, 6, 2, 6, 4, 2, 2, 6, 2, 2, 6, 2, 2, 12, 2, 2, 2, 4, 4, 6, 2, 2, 8, 6, 2, 6, 2, 2, 6, 2, 2, 12, 1, 6, 6, 2, 2, 6, 6, 2, 4, 2, 2, 12, 2, 6, 6, 2, 2, 16, 2, 2, 6, 6, 2, 6, 2, 2, 12, 6, 2, 6, 2, 6, 2, 2, 4, 12, 4, 2, 6, 2, 2, 30

Offset: 1

Author

Antti Karttunen, Jul 11 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000265, A001227, A005087, A046523, A064989, A087436, A336156, A336157, A336159, A336160.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));

Python

from math import prod
from sympy import factorint, prime
def A336158(n): return prod(prime(i+1)**e for i,e in enumerate(sorted(factorint(n>>(~n&n-1).bit_length()).values(),reverse=True))) # Chai Wah Wu, Sep 16 2022

Formula

a(n) = A046523(A000265(n)) = A046523(A064989(n)).

A000005(a(n)) = A001227(n).

A001221(a(n)) = A005087(n).

A001222(a(n)) = A087436(n).