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

1,4

Comments

Möbius transform of A000265(A156552(n)).

Links

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

Formula

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

Prog

(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));

Crossrefs

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

Sequence in context: A319162 A029171 A354185 * A256147 A079786 A032451

Adjacent sequences: A322991 A322992 A322993 * A322995 A322996 A322997

Keyword

nonn

Author

Antti Karttunen, Jan 02 2019

Status

approved