[go: up one dir, main page]

login
A324811
a(n) = A324728(n) - A061395(n).
2
0, 0, 0, 2, 0, 1, 0, 3, 2, 1, 0, 2, 0, 1, 2, 4, 0, 1, 0, 2, 2, 1, 0, 3, 2, 1, 3, 2, 0, 3, 0, 5, 1, 1, 2, 4, 0, 1, 2, 3, 0, 1, 0, 2, 3, 1, 0, 4, 2, 1, 1, 2, 0, 1, 2, 3, 2, 1, 0, 2, 0, 1, 1, 6, 1, 2, 0, 2, 1, 1, 0, 5, 0, 1, 3, 2, 2, 1, 0, 4, 5, 1, 0, 3, 2, 1, 2, 3, 0, 4, 2, 2, 1, 1, 2, 5, 0, 1, 3, 4, 0, 2, 0, 3, 3
OFFSET
1,4
COMMENTS
The first negative term is a(182) = -6, as A324712(182) = 0 and 182 = 2*7*13 = prime(1) * prime(4) * prime(6).
The next negative term after that is a(198) = -4, as A324712(198) = 1, and 198 = 2 * 3^2 * 11 = prime(1) * prime(2)^2 * prime(5).
There are only 161 negative terms among the first 10000 terms.
FORMULA
a(n) = A324728(n) - A061395(n).
a(p) = 0 for all primes p.
PROG
(PARI)
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
A324712(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A323243(d)))); (v); }; \\ Needs also code from A323243.
A000523(n) = if( n<1, 0, #binary(n) - 1); \\ From A000523
A324728(n) = { my(k=A324712(n)); if(!k, k, (1+A000523(k))); };
A324811(n) = (A324728(n) - A061395(n));
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Mar 17 2019
STATUS
approved