A353517 The largest proper divisor of A276086(2*n) reduced modulo 4, where A276086(n) the primorial base exp-function.

1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1

Offset: 0

Author

Antti Karttunen, Apr 24 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences related to primorial base

Crossrefs

Even bisection of A353516. Sequence A353487 shifted one term right.

Cf. A010873, A032742, A276086, A324895, A353527.

Programs

PARI

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A324895(n) = A032742(A276086(n));
A353517(n) = (A324895(2*n)%4);

Formula

a(n) = A353516(2*n) = A010873(A324895(2*n)).

For n >= 1, a(n) = (A353487(n) * A353527(n)) mod 4.

For n >= 1, a(n) = A353487(n-1). [See A353516 for a proof]