A324120 Binary weight of SumXOR variant of A297168: a(n) = A000120(A324180(n)).

0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 0, 2, 0, 2, 2, 3, 0, 2, 0, 2, 2, 2, 0, 2, 1, 2, 2, 2, 0, 2, 0, 4, 2, 2, 2, 3, 0, 2, 2, 4, 0, 2, 0, 2, 2, 2, 0, 2, 1, 2, 2, 2, 0, 2, 2, 4, 2, 2, 0, 4, 0, 2, 2, 5, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 4, 3, 2, 0, 4, 2, 2, 2, 4, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 3, 0, 2, 0, 4, 2

Offset: 1

Author

Antti Karttunen, Feb 19 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000043, A324179, A324180, A324181, A324190, A324191, A324192, A324201.

Programs

PARI

A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1));
A297112(n) = if(1==n, 0, 2^A297167(n));
A324180(n) = { my(v=0); fordiv(n, d, if(dA297112(d)))); (v); };
A324120(n) = hammingweight(A324180(n));

Formula

a(n) = A000120(A324180(n)).

a(n) <= A324190(n).

a(p^k) = k-1 for all primes p and exponents k >= 1.