A066423 Composite numbers n such that the product of proper divisors of the n does not equal n.
4, 9, 12, 16, 18, 20, 24, 25, 28, 30, 32, 36, 40, 42, 44, 45, 48, 49, 50, 52, 54, 56, 60, 63, 64, 66, 68, 70, 72, 75, 76, 78, 80, 81, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 116, 117, 120, 121, 124, 126, 128, 130, 132
Offset: 1
Keywords
Examples
The fourth composite number is 9. Its proper or aliquot divisors are 1 and 3. The product of 1 and 3 equals 3 which is not equal to 9. Therefore 9 is in the sequence.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..2000
Programs
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Mathematica
Composite[n_] := FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] + 1]; Do[m = Composite[n]; If[ Apply[ Times, Drop[ Divisors[m], -1]] != m, Print[m]], {n, 1, 100} ] Select[Range[150],CompositeQ[#]&&Times@@Most[Divisors[#]]!=#&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 18 2020 *) -
PARI
is(n)=my(d=numdiv(n)); d>4 || d==3 \\ Charles R Greathouse IV, Oct 15 2015
Comments