A324867 a(n) = A156552(n) XOR A324865(n), where XOR is bitwise-xor, A003987.

0, 1, 3, 2, 7, 4, 15, 6, 0, 13, 31, 10, 63, 16, 2, 6, 127, 12, 255, 18, 7, 46, 511, 22, 28, 82, 4, 46, 1023, 30, 2047, 30, 54, 174, 2, 22, 4095, 256, 12, 54, 8191, 36, 16383, 66, 24, 798, 32767, 46, 60, 31, 248, 130, 65535, 28, 19, 70, 12, 1300, 131071, 42, 262143, 2734, 48, 22, 126, 94, 524287, 302, 774, 40, 1048575, 38, 2097151, 4354, 10

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. A001065, A003986, A156552, A318457, A323243, A324865, A324866, A324398, 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
A318457(n) = bitxor(n,sigma(n)-n);
A324867(n) = if(1==n,0,A318457(A156552(n)));

PARI

A324867(n) = { my(k=A156552(n)); bitxor(k,(A323243(n)-k)); }; \\ Needs also code from A323243.

Formula

a(1) = 0; for n > 1, a(n) = A318457(A156552(n)).

a(n) = A156552(n) XOR (A323243(n) - A156552(n)).

a(n) = A323243(n) - 2*A324398(n).