A353564 Product_{d|n, dA276086(phi(d)), where A276086 is primorial base exp-function, and phi is Euler totient function.

1, 2, 2, 4, 2, 12, 2, 12, 6, 36, 2, 108, 2, 20, 54, 108, 2, 180, 2, 972, 30, 180, 2, 8748, 18, 100, 30, 300, 2, 43740, 2, 1620, 270, 900, 90, 24300, 2, 500, 150, 131220, 2, 22500, 2, 24300, 4050, 4500, 2, 1968300, 10, 121500, 1350, 7500, 2, 112500, 810, 67500, 750, 22500, 2, 265720500, 2, 28, 3750, 364500, 450

Offset: 1

Author

Antti Karttunen, Apr 27 2022

Keywords

• nonn

Links

• Index entries for sequences related to primorial base

Crossrefs

Cf. A000010, A051953, A276085, A276086, A353563, A353565 (rgs-transform).

Cf. also A318834.

Programs

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A353564(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A276086(eulerphi(d)))); m; };

Formula

a(1) = 1 (as an empty product).

a(n) = Product_{d|n, dA353563(d).

For all n >= 1, A276085(a(n)) = A051953(n).