A371098 a(n) = gcd(2n+1, A276086(2n+1)), where A276086 is the primorial base exp-function.

1, 3, 1, 1, 3, 1, 1, 15, 1, 1, 3, 1, 25, 3, 1, 1, 3, 7, 1, 3, 1, 1, 15, 1, 7, 3, 1, 5, 3, 1, 1, 21, 1, 1, 3, 1, 1, 75, 7, 1, 3, 1, 5, 3, 1, 7, 3, 1, 1, 3, 1, 1, 105, 1, 1, 3, 1, 5, 3, 7, 1, 3, 1, 1, 3, 1, 7, 15, 1, 1, 3, 1, 5, 147, 1, 1, 3, 1, 1, 3, 7, 1, 15, 1, 1, 3, 1, 175, 3, 1, 1, 3, 1, 1, 21, 1, 1, 15, 1, 1, 3

Offset: 0

Author

Antti Karttunen, Mar 10 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384
• Index entries for sequences related to primorial base

Crossrefs

Odd bisection of A324198.

Cf. A276086.

Programs

Mathematica

f[x_] := Block[{m, i, n = x, p}, m = i = 1; While[n > 0, p = Prime[i]; m *= p^Mod[n, p]; n = Quotient[n, p]; i++]; m]; Array[GCD[2 # + 1, f[2 #]] &, 120, 0] (* Michael De Vlieger, Mar 10 2024 *)

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A371098(n) = gcd(n+n+1, A276086(n+n));

Formula

a(n) = gcd(2n+1, A276086(2n+1)) = gcd(2n+1, A276086(2n)).

a(n) = A324198(2n+1).