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A047727 Average divisor is an integer (A003601) and the number is refactorable (A033950). 2
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 (list; graph; refs; listen; history; text; internal format)
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: A174460 A045001 A116660 * A069810 A292896 A154768

Adjacent sequences:  A047724 A047725 A047726 * A047728 A047729 A047730

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved

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Last modified June 18 18:52 EDT 2019. Contains 324215 sequences. (Running on oeis4.)