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

1,3

Links

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

Index entries for sequences computed from prime indices

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)).

Example

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).

Prog

(Scheme, two implementations)
(definec (A277707 n) (cond ((= 1 n) 0) ((odd? (A067029 n)) (A055396 n)) (else (A277707 (A028234 n)))))
(define (A277707 n) (A055396 (A007913 n)))
(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

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.

Sequence in context: A135156 A328967 A358171 * A357634 A344616 A316524

Adjacent sequences: A277704 A277705 A277706 * A277708 A277709 A277710

Keyword

nonn

Author

Antti Karttunen, Oct 28 2016

Status

approved