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A324713 a(n) = 2*A156552(n) XOR A323243(n). 7
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 27 19:34 EDT 2021. Contains 347694 sequences. (Running on oeis4.)