A350074 Difference between the maximal digit in the primorial base expansion of n and the maximal exponent in the prime factorization of n.

1, 0, 0, 0, 1, 0, 0, -2, -1, 1, 1, 0, 1, 1, 1, -2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 3, 1, 2, 3, 0, 0, -4, 0, 1, 1, -1, 0, 0, 0, -1, 1, 1, 1, 0, 0, 1, 1, -1, 1, 1, 2, 1, 2, 1, 3, 1, 3, 3, 3, 0, 1, 1, 0, -4, 1, 1, 1, 0, 1, 1, 1, -1, 1, 1, 0, 0, 1, 2, 2, -1, -1, 2, 2, 2, 3, 3, 3, 1, 3, 1, 2, 1, 2, 2, 2, -2, 2, 1, 1, 1, 2, 2, 2, 0, 2

Offset: 1

Author

Antti Karttunen, Feb 01 2022

Keywords

• sign
• base

Links

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

Crossrefs

Cf. A051903, A276086, A328114.

Cf. A350075 (positions of negative terms), A350076 (of terms >= 0), A350070 (their characteristic function), A351038 (positions of terms <= 0), A351039 (their characteristic function).

Cf. also A351074.

Programs

PARI

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); };
A350074(n) = (A051903(A276086(n)) - A051903(n));

Formula

a(n) = A328114(n) - A051903(n) = A051903(A276086(n)) - A051903(n).