A322994 Möbius transform of A322993.

0, 1, 1, 2, 1, 3, 1, 4, 2, 7, 1, 4, 1, 15, 3, 8, 1, 6, 1, 8, 7, 31, 1, 8, 2, 63, 4, 16, 1, 5, 1, 16, 15, 127, 3, 8, 1, 255, 31, 16, 1, 9, 1, 32, 4, 511, 1, 16, 2, 14, 63, 64, 1, 12, 7, 32, 127, 1023, 1, 8, 1, 2047, 8, 32, 15, 17, 1, 128, 255, 13, 1, 16, 1, 4095, 6, 256, 3, 33, 1, 32, 8, 8191, 1, 16, 31, 16383, 511, 64, 1, 12, 7, 512, 1023

Offset: 1

Author

Antti Karttunen, Jan 02 2019

Keywords

• nonn

Comments

Möbius transform of A000265(A156552(n)).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192

Crossrefs

Cf. A000265, A008683, A156552, A297112, A322993.

Programs

PARI

A000265(n) = (n/2^valuation(n, 2));
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))));
A322993(n) = if(1==n,0,A000265(A156552(n)));
A322994(n) = sumdiv(n,d,moebius(n/d)*A322993(d));

Formula

a(n) = Sum_{d|n} A008683(n/d)*A322993(d).