A374778 Denominator of the mean abundancy index of the divisors of n.

1, 4, 6, 12, 10, 24, 14, 32, 27, 8, 22, 72, 26, 56, 60, 80, 34, 54, 38, 120, 4, 88, 46, 192, 75, 104, 54, 56, 58, 48, 62, 64, 132, 136, 28, 162, 74, 152, 52, 320, 82, 16, 86, 264, 135, 184, 94, 160, 49, 30, 204, 104, 106, 216, 20, 64, 76, 232, 118, 720, 122, 248

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

For n = 2, n has 2 divisors, 1 and 2. Their abundancy indices are sigma(1)/1 = 1 and sigma(2)/2 = 3/2, and their mean abundancy index is (1 + 3/2)/2 = 5/4. Therefore a(2) = denominator(5/4) = 4.

Mathematica

f[p_, e_] := ((e+1)*p^2 - (e+2)*p + p^(-e))/((e+1)*(p-1)^2); a[1] = 1; a[n_] := Denominator[Times @@ f @@@ FactorInteger[n]]; Array[a, 100]

Prog

(PARI) a(n) = {my(f = factor(n), p, e); denominator(prod(i = 1, #f~, p = f[i, 1]; e = f[i, 2]; ((e+1)*p^2 - (e+2)*p + p^(-e))/((e+1)*(p-1)^2))); }

Crossrefs

Cf. A374777 (numerators).

Sequence in context: A189765 A074162 A365648 * A038040 A143356 A058270

Adjacent sequences: A374775 A374776 A374777 * A374779 A374780 A374781

Keyword

nonn,easy,frac

Author

Amiram Eldar, Jul 19 2024

Status

approved