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A324876
Xor-Moebius transform of A324866, where A324866(n) = A156552(n) OR (A323243(n) - A156552(n)).
7
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)).
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); };
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 18 2019
STATUS
approved