A328391 Maximal exponent in the prime factorization of A327860(n): a(n) = A051903(A327860(n)).

0, 0, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 2, 1, 1, 4, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 0, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 2, 2, 7, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 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. A002110, A003415, A051903, A276086, A327860, A327969, A328114, A328388, A328389, A328390, A328392.

Programs

PARI

A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
A328391(n) = A051903(A327860(n));

Formula

a(n) = A051903(A327860(n)) = A051903(A003415(A276086(n))).

a(A002110(n)) = 0 for all n >= 0.

For all n >= 1, a(n) >= A328114(n)-1. [Because arithmetic derivative will decrease the maximal prime exponent (A051903) of its argument by at most one]