A324878 Xor-Moebius transform of A324398, where A324398(n) = A156552(n) AND (A323243(n) - A156552(n)).

0, 0, 0, 1, 0, 1, 0, 0, 6, 0, 0, 1, 0, 1, 8, 8, 0, 6, 0, 0, 16, 1, 0, 0, 0, 1, 12, 1, 0, 8, 0, 8, 0, 1, 20, 8, 0, 1, 66, 0, 0, 17, 0, 1, 8, 1, 0, 8, 0, 0, 2, 1, 0, 12, 36, 0, 258, 1, 0, 0, 0, 1, 16, 40, 0, 1, 0, 1, 0, 20, 0, 24, 0, 1, 24, 1, 32, 67, 0, 8, 0, 1, 0, 1, 132, 1, 1026, 0, 0, 40, 72, 1, 0, 1, 256, 16, 0, 1, 68, 16, 0, 3, 0, 0, 46

Offset: 1

Author

Antti Karttunen, Mar 18 2019

Keywords

• nonn

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. A156552, A318458, A324820, A324821, A324876, A324877.

Programs

PARI

A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A318458(n) = bitand(n, sigma(n)-n);
A324398(n) = if(1==n,0,A318458(A156552(n)));
\\ Or, equivalently:
A324398(n) = { my(k=A156552(n)); bitand(k,(A323243(n)-k)); }; \\ Needs also code from A323243.
A324878(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A324398(d)))); (v); };

Formula

a(p) = 0 for all primes p.