A324180 SumXOR variant of A297168.

0, 0, 0, 1, 0, 3, 0, 3, 2, 5, 0, 3, 0, 9, 6, 7, 0, 5, 0, 3, 10, 17, 0, 3, 4, 33, 6, 3, 0, 5, 0, 15, 18, 65, 12, 7, 0, 129, 34, 15, 0, 9, 0, 3, 6, 257, 0, 3, 8, 9, 66, 3, 0, 9, 20, 23, 130, 513, 0, 15, 0, 1025, 6, 31, 36, 17, 0, 3, 258, 9, 0, 3, 0, 2049, 10, 3, 24, 33, 0, 23, 14, 4097, 0, 23, 68, 8193, 514, 39, 0, 9, 40, 3

Offset: 1

Author

Antti Karttunen, Feb 19 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4096
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A061395, A156552, A297106, A297112, A297167, A297168, A324181 (rgs-transform), A324120 (number of 1-bits).

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); };

Formula

a(n) = Cumulative XOR of A297112(d), where d ranges over the proper divisors d of n.