A324713 a(n) = 2*A156552(n) XOR A323243(n).

0, 3, 7, 2, 15, 12, 31, 6, 0, 31, 63, 26, 127, 48, 6, 6, 255, 20, 511, 50, 3, 114, 1023, 54, 4, 214, 4, 118, 2047, 10, 4095, 30, 114, 434, 2, 30, 8191, 768, 20, 118, 16383, 108, 32767, 194, 8, 1826, 65535, 110, 12, 45, 504, 386, 131071, 36, 19, 198, 20, 3348, 262143, 122, 524287, 6834, 112, 22, 246, 234, 1048575, 822, 1794, 120

Offset

1,2

Comments

a(n) is also the cumulative XOR of (2*A297106(d) XOR A324712(d)) over the divisors d of n.

It is conjectured that a(n) may obtain value zero only when n is a power of prime, and especially for n > 1, it must be a prime power present in A324201.

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)

Formula

a(n) = 2*A156552(n) XOR A323243(n).

a(n) = XORsum_{d|n} (2*A297106(d) XOR A324712(d)).

Prog

(PARI) A324713(n) = { my(x=0, s=0); fordiv(n, d, x = bitxor(x, A324712(d)); s = bitxor(s, A297106(d))); bitxor(x, 2*s); };

Crossrefs

Cf. A003987, A156552, A297106, A323243, A323244, A324201, A324712, A324714.

Sequence in context: A237427 A210203 A318467 * A245611 A063041 A257729

Adjacent sequences: A324710 A324711 A324712 * A324714 A324715 A324716

Keyword

nonn

Author

Antti Karttunen, Mar 13 2019

Status

approved