A353497 The smallest prime factor of n, reduced modulo 4, with a(1) = 1.

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

Offset: 1

Author

Antti Karttunen, Apr 26 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A010873, A020639, A353490, A353526.

Cf. also A353493.

Programs

Mathematica

a[n_] := Mod[FactorInteger[n][[1, 1]], 4]; Array[a, 100] (* Amiram Eldar, Apr 26 2022 *)

PARI

A020639(n) = if(1==n,n,vecmin(factor(n)[, 1]));
A353497(n) = (A020639(n)%4);

Python

from sympy import factorint
def a(n): return 1 if n==1 else (2 if n%2==0 else min(factorint(n))%4)
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Apr 26 2022

Formula

a(n) = A010873(A020639(n)).

For all n >= 1, A010873(n) = A010873(A353490(n)*a(n)).

For all n >= 1, a(2n-1) = A010873(A353490(2n-1)*(2n-1)).

For all n >= 1, a(A276086(n)) = A353526(n).