A329034 Möbius transform of A122111.

1, 1, 3, 1, 7, 1, 15, 2, 5, 3, 31, 3, 63, 7, 7, 2, 127, 4, 255, 7, 17, 15, 511, 2, 19, 31, 16, 15, 1023, 7, 2047, 4, 37, 63, 31, 2, 4095, 127, 77, 6, 8191, 15, 16383, 31, 27, 255, 32767, 6, 65, 14, 157, 63, 65535, 4, 69, 14, 317, 511, 131071, 1, 262143, 1023, 59, 2, 145, 31, 524287, 127, 637, 25, 1048575, 8, 2097151, 2047, 38, 255, 115, 63

Offset: 1

Author

Antti Karttunen, Nov 08 2019

Keywords

• sign

Comments

a(144) = -2 is the first negative term.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4096
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A008683, A122111, A329035.

Cf. also A297112.

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)));
A329034(n) = sumdiv(n,d,moebius(n/d)*A122111(d));

Formula

a(n) = Sum_{d|n} A008683(n/d)*A122111(d).