A324876 Xor-Moebius transform of A324866, where A324866(n) = A156552(n) OR (A323243(n) - A156552(n)).

0, 1, 3, 2, 7, 7, 15, 4, 5, 11, 31, 12, 63, 31, 14, 8, 127, 13, 255, 28, 27, 49, 511, 24, 27, 109, 8, 60, 1023, 24, 2047, 16, 42, 209, 30, 28, 4095, 511, 114, 32, 8191, 43, 16383, 110, 17, 737, 32767, 48, 51, 9, 134, 210, 65535, 24, 47, 108, 498, 1771, 131071, 38, 262143, 3409, 36, 32, 70, 94, 524287, 386, 762, 42, 1048575, 52, 2097151, 7933, 11

Offset

1,3

Comments

It seems that the records, which are A000225(n) = 2^n - 1 occur at primes, as occur also the records for the width of terms, A000523(a(n)), and the records for the binary weights 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(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
A318456(n) = bitor(n, sigma(n)-n);
A324866(n) = if(1==n, 0, A318456(A156552(n)));
A324876(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A324866(d)))); (v); };

Crossrefs

Cf. A156552, A323243, A324820, A324821, A324866, A324877, A324878.

Sequence in context: A198552 A120633 A095353 * A226370 A054183 A357939

Adjacent sequences: A324873 A324874 A324875 * A324877 A324878 A324879

Keyword

nonn

Author

Antti Karttunen, Mar 18 2019

Status

approved