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A353497
The smallest prime factor of n, reduced modulo 4, with a(1) = 1.
2
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
1,2
LINKS
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).
MATHEMATICA
a[n_] := Mod[FactorInteger[n][[1, 1]], 4]; Array[a, 100] (* Amiram Eldar, Apr 26 2022 *)
PROG
(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
CROSSREFS
Cf. also A353493.
Sequence in context: A032452 A084199 A277745 * A320858 A304111 A030314
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 26 2022
STATUS
approved