A324713 - OEIS

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

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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.