A297172 Möbius transform of A253564.

0, 1, 3, 1, 7, 1, 15, 2, 3, 3, 31, 3, 63, 7, 3, 4, 127, 2, 255, 7, 9, 15, 511, 6, 7, 31, 6, 15, 1023, 3, 2047, 8, 21, 63, 7, 4, 4095, 127, 45, 14, 8191, 7, 16383, 31, 9, 255, 32767, 12, 15, 4, 93, 63, 65535, 4, 21, 30, 189, 511, 131071, 5, 262143, 1023, 21, 16, 49, 15, 524287, 127, 381, 5, 1048575, 8, 2097151, 2047, 6

Offset

1,3

Links

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

Formula

a(n) = Sum_{d|n} A008683(n/d)*A253564(d).

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)};
A122111(n) = if(1==n, n, prime(bigomega(n))*A122111(A064989(n)));
A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
A253564(n) = A156552(A122111(n));
A297172(n) = sumdiv(n, d, moebius(n/d)*A253564(d));

Crossrefs

Cf. A008683, A064989, A122111, A156552, A253564, A297162 (rgs-transform of this sequence).

Cf. also A297112, A297156, A297171.

Sequence in context: A089736 A205479 A094024 * A329034 A353961 A290678

Adjacent sequences: A297169 A297170 A297171 * A297173 A297174 A297175

Keyword

nonn

Author

Antti Karttunen, Dec 26 2017

Status

approved