A351074 Difference between the maximal exponent in the prime factorization of A327860(n) and the maximal exponent in the prime factorization of n.

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

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, A327860, A328114, A328391.

Cf. A351075 (positions of negative terms), A351076 (of terms >= 0), A351077 (their characteristic function).

Cf. also A350074.

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); };
A351074(n) = (A051903(A327860(n)) - A051903(n));

Formula

a(n) = A328391(n) - A051903(n) = A051903(A327860(n)) - A051903(n).