A353497 - OEIS

%I #15 Apr 27 2022 13:55:02

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A353497/b353497.txt">Table of n, a(n) for n = 1..65537</a>

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

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

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

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

%t a[n_] := Mod[FactorInteger[n][[1, 1]], 4]; Array[a, 100] (* _Amiram Eldar_, Apr 26 2022 *)

%o (PARI)

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

%o A353497(n) = (A020639(n)%4);

%o (Python)

%o from sympy import factorint

%o def a(n): return 1 if n==1 else (2 if n%2==0 else min(factorint(n))%4)

%o print([a(n) for n in range(1, 106)]) # _Michael S. Branicky_, Apr 26 2022

%Y Cf. A010873, A020639, A353490, A353526.

%Y Cf. also A353493.

%K nonn

%O 1,2

%A _Antti Karttunen_, Apr 26 2022