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

1,2

Links

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

Formula

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

Prog

(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);
(Scheme) (define (A286584 n) (modulo (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

Crossrefs

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

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

Sequence in context: A070078 A054438 A261015 * A174947 A010341 A072772

Adjacent sequences: A286581 A286582 A286583 * A286585 A286586 A286587

Keyword

nonn

Author

Antti Karttunen, May 31 2017

Status

approved