A277708 a(n) = Least prime divisor of n with an odd exponent, or 1 if n is a perfect square.

1, 2, 3, 1, 5, 2, 7, 2, 1, 2, 11, 3, 13, 2, 3, 1, 17, 2, 19, 5, 3, 2, 23, 2, 1, 2, 3, 7, 29, 2, 31, 2, 3, 2, 5, 1, 37, 2, 3, 2, 41, 2, 43, 11, 5, 2, 47, 3, 1, 2, 3, 13, 53, 2, 5, 2, 3, 2, 59, 3, 61, 2, 7, 1, 5, 2, 67, 17, 3, 2, 71, 2, 73, 2, 3, 19, 7, 2, 79, 5, 1, 2, 83, 3, 5, 2, 3, 2, 89, 2, 7, 23, 3, 2, 5, 2, 97, 2, 11, 1, 101, 2, 103, 2, 3

Offset: 1

Author

Antti Karttunen, Oct 28 2016

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A020639, A007913, A008578, A277707.

Cf. A000290 (after its initial zero-term gives the positions of ones in this sequence).

Cf. also A277698.

Programs

PARI

a(n) = my(f = factor(core(n))); if (!#f~, 1, vecmin(f[,1])); \\ Michel Marcus, Oct 30 2016

Python

from sympy import primefactors
from sympy.ntheory.factor_ import core
def lpf(n): return 1 if n==1 else primefactors(n)[0]
def a(n): return lpf(core(n)) # Indranil Ghosh, May 17 2017

Formula

a(n) = A008578(1+A277707(n)).

a(n) = A020639(A007913(n)).