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
Keywords
Examples
x = 56, sigma(x) = 120, number of divisors of x = 8. 120/8 and 56/8 are integers.
Links
- Donovan Johnson, Table of n, a(n) for n = 1..10000
Programs
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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 *) -
PARI
isok(n) = my(d = numdiv(n)); !(n % d) && !(sigma(n) % d); \\ Michel Marcus, Oct 15 2016
Formula
Both sigma_1(x)/sigma_0(x) and x/sigma_0(x) are integers. - clarified by Harvey P. Dale, Apr 27 2012