A324821 Xor-Moebius transform of A324819, where A324819(n) = bitor(2*A156552(n), A323243(n)), where bitor is A003986.

0, 3, 7, 5, 15, 10, 31, 8, 11, 19, 63, 21, 127, 46, 30, 16, 255, 27, 511, 44, 63, 78, 1023, 40, 19, 170, 16, 65, 2047, 38, 4095, 32, 78, 334, 58, 48, 8191, 766, 236, 64, 16383, 110, 32767, 177, 49, 1246, 65535, 80, 35, 51, 260, 341, 131071, 48, 107, 176, 1004, 2794, 262143, 104, 524287, 5454, 80, 64, 142, 219, 1048575, 641, 1278, 110

Offset

1,2

Comments

It seems that the records, which are A000225(1+n) = 2^(1+n) - 1 occur at primes, as occur also the records for the width of terms, A000523(a(n)), and the records for the binary weight of terms, A000120(a(n)).

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(A000040(n)) = A000225(1+n).

Prog

(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 by David A. Corneth
A324819(n) = bitor(2*A156552(n), A323243(n)); \\ Needs code also from A323243.
A324821(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A324819(d)))); (v); };

Crossrefs

Cf. A003986, A156552, A323243, A324815, A324819, A324820, A324876, A324878.

Sequence in context: A342701 A184162 A369277 * A345401 A059912 A354008

Adjacent sequences: A324818 A324819 A324820 * A324822 A324823 A324824

Keyword

nonn

Author

Antti Karttunen, Mar 18 2019

Status

approved