A342026 Difference in the maximal prime exponents between the arithmetic derivative of A276086(n) and A276086(n) itself, which is the prime product form of primorial base expansion of n.

-1, -1, 0, -1, -1, -1, 0, 2, 0, -1, -1, -1, 0, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 0, 0, -1, -1, 1, 0, 0, 0, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, 0, -1, 1, -1, -1, -1, -1, -1, -1, -1, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1

Offset: 1

Author

Antti Karttunen, Mar 13 2021

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A276086, A342005, A327860, A328114, A328310, A328391, A342006 (positions of nonnegative terms).

Cf. also A342016, A342019.

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) = if(!n,n,A051903(A327860(n)));
A328114(n) = { my(s=0, p=2); while(n, s = max(s, (n%p)); n = n\p; p = nextprime(1+p)); (s); };
A342026(n) = (A328391(n) - A328114(n));

Formula

a(n) = A328310(A276086(n)) = A328391(n) - A328114(n).

a(n) = -1 iff A342005(n) = 1.