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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

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 * A072498 A162643 A072587

Adjacent sequences:  A066420 A066421 A066422 * A066424 A066425 A066426

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Dec 26 2001

STATUS

approved

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Last modified March 3 04:22 EST 2021. Contains 341756 sequences. (Running on oeis4.)