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

1,3

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

Formula

a(n) = Sum_{d|n} A008683(n/d)*A122111(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)));
A329034(n) = sumdiv(n, d, moebius(n/d)*A122111(d));

Crossrefs

Cf. A008683, A122111, A329035.

Cf. also A297112.

Sequence in context: A205479 A094024 A297172 * A353961 A290678 A290422

Adjacent sequences: A329031 A329032 A329033 * A329035 A329036 A329037

Keyword

sign

Author

Antti Karttunen, Nov 08 2019

Status

approved