A371099 a(n) = gcd(36*n+9, A276086(36*n+9)), where A276086 is the primorial base exp-function.

3, 15, 3, 3, 3, 21, 75, 3, 33, 3, 3, 15, 3, 3, 3, 3, 15, 3, 3, 231, 3, 15, 3, 3, 3, 3, 105, 3, 3, 3, 363, 75, 3, 21, 3, 3, 15, 3, 3, 3, 21, 165, 3, 3, 3, 3, 15, 3, 3, 3, 3, 15, 33, 3, 21, 3, 75, 3, 3, 3, 3, 735, 3, 33, 3, 3, 15, 3, 273, 3, 3, 15, 3, 3, 33, 21, 15, 3, 3, 3, 3, 975, 3, 3, 3, 33, 15, 3, 3, 21, 3, 15

Offset: 0

Author

Antti Karttunen, Mar 10 2024

Keywords

• nonn

Comments

All terms are multiples of 3, with A007949(a(n)) = 1 for all n.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..11550
• Index entries for sequences related to primorial base

Crossrefs

Cf. A007949, A139609, A276086, A324198.

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[#, f[#]] &[36 # + 9] &, 100, 0] (* Michael De Vlieger, Mar 10 2024, after Jean-François Alcover at A276086 *)

PARI

A324198(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (m); };
A371099(n) = A324198((36*n)+9);

Formula

a(n) = A324198(A139609(n)).