A324811 a(n) = A324728(n) - A061395(n).

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

Author

Antti Karttunen, Mar 17 2019

Keywords

• sign

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000523, A061395, A323243, A324712, A324728.

Programs

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));

Formula

a(n) = A324728(n) - A061395(n).

a(p) = 0 for all primes p.