A331289 a(n) = A329348(n) - A001222(n).

1, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 1, 0, 0, 4, -2, 0, -1, 0, 1, 4, 0, 0, -1, 0, 0, -2, 1, 0, 2, 0, -4, 4, 0, 6, 0, 0, 0, 4, -3, 0, -2, 0, 1, -2, 0, 0, -4, -1, 1, 4, 1, 0, -2, 2, 4, 4, 0, 0, -1, 0, 0, 0, -4, 11, 9, 0, 1, 4, 2, 0, -2, 0, 0, 2, 1, 0, 9, 0, -3, -3, 0, 0, -2, 9, 0, 4, 4, 0, -2, 4, 1, 4, 0, 5, -4, 0, -1, 7, -3, 0, 9, 0, 4, 1

Offset: 1

Author

Antti Karttunen, Jan 15 2020

Keywords

• sign
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12571
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A001222, A117366, A329348, A329619, A331188, A331290.

Programs

PARI

A002110(n) = prod(i=1, n, prime(i));
A331289(n) = if(1==n, 1, my(f=factor(n), p=nextprime(1+vecmax(f[, 1]))); (prod(i=1, #f~, A002110(primepi(f[i, 1]))^(f[i, 2]-(#f~==i)))%p)-bigomega(n));

Formula

a(n) = A329348(n) - A001222(n).

a(n) = (A331188(n) mod A117366(n)) - A001222(n).