A328390 Maximal digit value in primorial base expansion of the arithmetic derivative of n: a(n) = A328114(A003415(n)).

0, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 4, 2, 2, 1, 2, 2, 2, 4, 1, 1, 1, 1, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 3, 1, 4, 1, 3, 2, 2, 3, 4, 1, 3, 2, 3, 3, 1, 1, 3, 1, 1, 3, 6, 3, 2, 1, 2, 4, 4, 1, 5, 1, 1, 4, 3, 3, 2, 1, 5, 3, 2, 1, 4, 3, 2, 1, 4, 1, 4, 3, 3, 2, 3, 4, 2, 1, 2, 2, 4, 1, 3, 1, 5, 2

Offset: 1

Author

Antti Karttunen, Oct 15 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..30030
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A051903, A327859, A328114, A328389, A328391, A328392.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A328114(n) = { my(s=0, p=2); while(n, s = max(s,(n%p)); n = n\p; p = nextprime(1+p)); (s); };
A328390(n) = A328114(A003415(n));

Formula

a(n) = A328114(A003415(n)).

a(n) = A051903(A327859(n)).