A047727 Average divisor is an integer (A003601) and the number is refactorable (A033950).

1, 56, 60, 96, 132, 184, 204, 248, 276, 348, 376, 480, 492, 504, 564, 568, 612, 632, 636, 672, 708, 824, 852, 864, 996, 1016, 1056, 1068, 1208, 1212, 1248, 1284, 1336, 1356, 1520, 1528, 1572, 1592, 1632, 1644, 1656, 1784, 1788, 1824, 1908, 1912, 1980

Offset

1,2

Links

Donovan Johnson, Table of n, a(n) for n = 1..10000

Formula

Both sigma_1(x)/sigma_0(x) and x/sigma_0(x) are integers. - clarified by Harvey P. Dale, Apr 27 2012

Example

x = 56, sigma(x) = 120, number of divisors of x = 8. 120/8 and 56/8 are integers.

Mathematica

adiQ[n_]:=Module[{ds1=DivisorSigma[1, n], ds0=DivisorSigma[0, n]} , Divisible[ ds1, ds0]&&Divisible[n, ds0]]; Select[Range[2000], adiQ] (* Harvey P. Dale, Apr 27 2012 *)

Prog

(PARI) isok(n) = my(d = numdiv(n)); !(n % d) && !(sigma(n) % d); \\ Michel Marcus, Oct 15 2016

Crossrefs

Cf. A007691, A001599, A046985.

Sequence in context: A345495 A045001 A116660 * A069810 A292896 A154768

Adjacent sequences: A047724 A047725 A047726 * A047728 A047729 A047730

Keyword

nonn

Author

Labos Elemer

Status

approved