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

1,1

Comments

A084115(a(n))>1; complement of A084116. - Reinhard Zumkeller, May 12 2003

Links

Harvey P. Dale, Table of n, a(n) for n = 1..2000

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

(PARI) is(n)=my(d=numdiv(n)); d>4 || d==3 \\ Charles R Greathouse IV, Oct 15 2015

Crossrefs

Cf. A048741, A007422.

Sequence in context: A312854 A010386 A094120 * A355571 A376164 A072498

Adjacent sequences: A066420 A066421 A066422 * A066424 A066425 A066426

Keyword

nonn

Author

Robert G. Wilson v, Dec 26 2001

Status

approved