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

Author

Antti Karttunen, Dec 26 2017

Keywords

• nonn

Links

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

Crossrefs

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

Cf. also A297112, A297156, A297171.

Programs

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));

Formula

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