A351097 Difference between {the maximal digit value in primorial base expansion of the arithmetic derivative of n} and {the maximal exponent in the prime factorization of n}.

0, 0, 0, 0, 0, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, -3, 0, 1, 0, 2, 1, 1, 0, -1, 0, 1, 1, -1, 0, 0, 0, -2, 1, 2, 1, 0, 0, 2, 1, -1, 0, 1, 0, 1, -1, 3, 0, -1, 0, 0, 2, 2, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 1, 0, 2, 1, 0, 0, 3, 3, 0, 2, 0, 0, 2, 1, 2, 1, 0, 1, -1, 1, 0, 2, 2, 1, 0, 1, 0, 2, 2, 1, 1, 2, 3, -3, 0, 0, 0, 2, 0, 2, 0, 2, 1

Offset: 1

Author

Antti Karttunen, Feb 03 2022

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..30030

Crossrefs

Cf. A003415, A051903, A276086, A327859, A328390, A351098 (positions of negative terms), A351099.

Cf. also A350074, A351074.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A051903(n) = if((1==n),0,vecmax(factor(n)[, 2]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A327859(n) = A276086(A003415(n));
A351097(n) = (A051903(A327859(n)) - A051903(n));

Formula

a(n) = A328390(n) - A051903(n) = A051903(A327859(n)) - A051903(n).