

A066423


Composite numbers n such that the product of proper divisors of the n does not equal n.


3



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS



LINKS



EXAMPLE

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.


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 *)


PROG



CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



