A277707 a(n) = index of the least prime divisor of n which has an odd exponent, or 0 if n is a perfect square.

0, 1, 2, 0, 3, 1, 4, 1, 0, 1, 5, 2, 6, 1, 2, 0, 7, 1, 8, 3, 2, 1, 9, 1, 0, 1, 2, 4, 10, 1, 11, 1, 2, 1, 3, 0, 12, 1, 2, 1, 13, 1, 14, 5, 3, 1, 15, 2, 0, 1, 2, 6, 16, 1, 3, 1, 2, 1, 17, 2, 18, 1, 4, 0, 3, 1, 19, 7, 2, 1, 20, 1, 21, 1, 2, 8, 4, 1, 22, 3, 0, 1, 23, 2, 3, 1, 2, 1, 24, 1, 4, 9, 2, 1, 3, 1, 25, 1, 5, 0, 26, 1, 27, 1, 2

Offset: 1

Author

Antti Karttunen, Oct 28 2016

Keywords

• nonn

Examples

			For n = 8 = 2*2*2 = prime(1)^3, the exponent of the least (and the only) prime factor 2 is 3, an odd number, thus a(8) = 1 as 2 = prime(1).
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from prime indices

Crossrefs

Cf. A007913, A028234, A055396, A067029.

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

Cf. also A277708, A277697.

Programs

PARI

a(n) = my(f = factor(core(n))); if (!#f~, 0, primepi(vecmin(f[,1]))); \\ Michel Marcus, Oct 30 2016

Python

from sympy import primepi, isprime, primefactors
from sympy.ntheory.factor_ import core
def a049084(n): return primepi(n)*(1*isprime(n))
def a055396(n): return 0 if n==1 else a049084(min(primefactors(n)))
def a(n): return a055396(core(n)) # Indranil Ghosh, May 17 2017

Formula

a(1) = 0; for n > 1, if A067029(n) is odd, then a(n) = A055396(n), otherwise a(n) = a(A028234(n)).

a(n) = A055396(A007913(n)).