A376416 a(n) = A276085(A006862(n)), where A276085 is the primorial base log-function, and A006862 is the Euclid numbers, one more than primorials.

1, 2, 30, 6469693230, 7799922041683461553249199106329813876687996789903550945093032474868511536164700810

Offset: 0

Author

Antti Karttunen, Nov 17 2024

Keywords

• nonn

Comments

Numbers k such that when we apply primorial base exp function (A276086) twice to them, the results are squarefree even semiprimes, A100484 after its initial 4. See comments in A377871.

a(5)..a(8) have 976, 209, 111, 12051 decimal digits.

a(n) is a primorial for those n that are in A014545, that is, when A006862(n) is one of the primorial primes, A018239.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..7
• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A002110, A006862, A014545, A018239, A100484, A276085, A276086, A276087, A377871.

Programs

PARI

A276085(n) = { my(f = factor(n), pr=1, i=1, s=0); for(k=1, #f~, while(i <= primepi(f[k, 1])-1, pr *= prime(i); i++); s += f[k, 2]*pr); (s); };
A376416(n) = A276085(1+prod(i=1,n,prime(i)));

Formula

a(n) = A276085(1+A002110(n)) = A276085(A276085(A100484(1+n))).

For n >= 1, A276087(a(n)) = A100484(1+n).