cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A066423 Composite numbers n such that the product of proper divisors of the n does not equal n.

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%I A066423 #10 Oct 18 2020 15:57:34
%S A066423 4,9,12,16,18,20,24,25,28,30,32,36,40,42,44,45,48,49,50,52,54,56,60,
%T A066423 63,64,66,68,70,72,75,76,78,80,81,84,88,90,92,96,98,99,100,102,104,
%U A066423 105,108,110,112,114,116,117,120,121,124,126,128,130,132
%N A066423 Composite numbers n such that the product of proper divisors of the n does not equal n.
%C A066423 A084115(a(n))>1; complement of A084116. - _Reinhard Zumkeller_, May 12 2003
%H A066423 Harvey P. Dale, <a href="/A066423/b066423.txt">Table of n, a(n) for n = 1..2000</a>
%e A066423 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.
%t A066423 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} ]
%t A066423 Select[Range[150],CompositeQ[#]&&Times@@Most[Divisors[#]]!=#&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Oct 18 2020 *)
%o A066423 (PARI) is(n)=my(d=numdiv(n)); d>4 || d==3 \\ _Charles R Greathouse IV_, Oct 15 2015
%Y A066423 Cf. A048741, A007422.
%K A066423 nonn
%O A066423 1,1
%A A066423 _Robert G. Wilson v_, Dec 26 2001