A297156 Möbius transform of A243354.

0, 1, 3, 1, 7, 2, 15, 3, 1, 6, 31, 6, 63, 14, 2, 5, 127, 2, 255, 14, 10, 30, 511, 10, 1, 62, 7, 30, 1023, 4, 2047, 11, 26, 126, 2, 2, 4095, 254, 58, 26, 8191, 12, 16383, 62, 14, 510, 32767, 22, 1, 2, 122, 126, 65535, 6, 18, 58, 250, 1022, 131071, 4, 262143, 2046, 30, 21, 50, 28, 524287, 254, 506, 4, 1048575, 6

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..4096

Prog

(PARI)
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
A006068(n)= { my(s=1, ns); while(1, ns = n >> s; if(0==ns, break()); n = bitxor(n, ns); s <<= 1; ); return (n); } \\ Essentially Joerg Arndt's Jul 19 2012 code.
A243354(n) = A006068(A156552(n));
A297156(n) = sumdiv(n, d, moebius(n/d)*A243354(d));

Crossrefs

Cf. A006068, A156552, A243354, A297157 (rgs-transform of this sequence).

Cf. also A297112, A297171, A297172.

Sequence in context: A065265 A235263 A297171 * A132885 A187818 A365454

Adjacent sequences: A297153 A297154 A297155 * A297157 A297158 A297159

Keyword

nonn

Author

Antti Karttunen, Dec 28 2017

Status

approved