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

1,2

Links

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

Formula

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

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

Prog

(Scheme, two different implementations)
(define (A277708 n) (A008578 (+ 1 (A277707 n))))
(define (A277708 n) (A020639 (A007913 n)))
(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

Crossrefs

Cf. A020639, A007913, A008578, A277707.

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

Cf. also A277698.

Sequence in context: A158584 A086112 A138798 * A360496 A356473 A328661

Adjacent sequences: A277705 A277706 A277707 * A277709 A277710 A277711

Keyword

nonn

Author

Antti Karttunen, Oct 28 2016

Status

approved