A286584 a(n) = A048673(n) mod 4.

1, 2, 3, 1, 0, 0, 2, 2, 1, 3, 3, 3, 1, 1, 2, 1, 2, 2, 0, 0, 0, 0, 3, 0, 1, 2, 3, 2, 0, 1, 3, 2, 1, 1, 3, 1, 1, 3, 3, 3, 2, 3, 0, 3, 0, 0, 3, 3, 1, 2, 0, 1, 2, 0, 2, 1, 2, 3, 3, 2, 2, 0, 2, 1, 0, 2, 0, 2, 1, 0, 1, 2, 0, 2, 3, 0, 0, 0, 2, 0, 1, 1, 1, 0, 3, 3, 2, 0, 1, 3, 2, 3, 1, 0, 1, 0, 3, 2, 3, 1, 0, 3, 2, 2, 1, 1, 3, 3, 1, 1, 3, 2, 0

Offset: 1

Author

Antti Karttunen, May 31 2017

Keywords

• nonn

Links

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

Crossrefs

Cf. A010873, A048673, A286582, A286583, A286585.

Cf. A246261 (positions of odd terms), A246263 (of even terms).

Programs

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ Using code of Michel Marcus
A048673(n) = (A003961(n)+1)/2;
A286584(n) = (A048673(n)%4);

Python

from sympy import factorint, nextprime
from operator import mul
def a048673(n):
    f = factorint(n)
    return 1 if n==1 else (1 + reduce(mul, [nextprime(i)**f[i] for i in f]))/2
def a(n): return a048673(n)%4 # Indranil Ghosh, Jun 12 2017

Scheme

(define (A286584 n) (modulo (A048673 n) 4))

Formula

a(n) = A010873(A048673(n)) = A048673(n) mod 4.