A349630 Denominators of the Dirichlet inverse of the abundancy index, sigma(n)/n.

1, 2, 3, 2, 5, 1, 7, 1, 3, 5, 11, 3, 13, 7, 5, 1, 17, 2, 19, 5, 21, 11, 23, 1, 5, 13, 1, 7, 29, 5, 31, 1, 11, 17, 35, 6, 37, 19, 39, 1, 41, 7, 43, 11, 5, 23, 47, 1, 7, 10, 17, 13, 53, 1, 55, 1, 57, 29, 59, 5, 61, 31, 21, 1, 65, 11, 67, 17, 23, 35, 71, 1, 73, 37, 15, 19, 77, 13, 79, 1, 1, 41, 83, 21, 85, 43, 29, 1, 89

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Mathematica

f[1] = 1; f[n_] := f[n] = -DivisorSum[n, f[#] * DivisorSigma[1, n/#] * #/n &, # < n &]; Denominator @ Array[f, 100] (* Amiram Eldar, Nov 28 2021 *)

Prog

(PARI)
up_to = 16384;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v, correctly!
Abi(n) = (sigma(n)/n);
vDirInv_of_Abi = DirInverseCorrect(vector(up_to, n, Abi(n)));
A349630(n) = denominator(vDirInv_of_Abi[n]);

Crossrefs

Cf. A000203, A017665, A017666.

Cf. A349629 (numerators).

Sequence in context: A368900 A014973 A276835 * A157753 A020500 A014963

Adjacent sequences: A349627 A349628 A349629 * A349631 A349632 A349633

Keyword

nonn,frac

Author

Antti Karttunen, Nov 27 2021

Status

approved