A369010 Exponential of Mangoldt function M(n) applied to primorial base exp-function: a(n) = A014963(A276086(n)).

1, 2, 3, 1, 3, 1, 5, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Antti Karttunen, Jan 14 2024

Keywords

• nonn

Comments

Also LCM-transform of A276086, because A276086 has the S-property explained in the comments of A368900.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..30030
• Index entries for sequences related to primorial base

Crossrefs

Cf. A014963, A060735 (positions of terms > 1), A276086, A368900.

Programs

PARI

A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A369010(n) = A014963(A276086(n));

PARI

up_to = 510511; \\ = 1+A002110(7);
LCMtransform(v) = { my(len = length(v), b = vector(len), g = vector(len)); b[1] = g[1] = 1; for(n=2,len, g[n] = lcm(g[n-1],v[n]); b[n] = g[n]/g[n-1]); (b); };
v369010 = LCMtransform(vector(up_to,n,A276086(n-1)));
A369010(n) = v369010[1+n];

Formula

a(n) = A014963(A276086(n)).

For n > 0, a(n) = lcm {1..A276086(n)} / lcm {1..A276086(n-1)}.