A137428 Positive integers n which have a composite divisor smaller than their largest prime factor.
20, 28, 40, 42, 44, 52, 56, 60, 66, 68, 76, 78, 80, 84, 88, 92, 99, 100, 102, 104, 110, 112, 114, 116, 117, 120, 124, 126, 130, 132, 136, 138, 140, 148, 152, 153, 156, 160, 164, 168, 170, 171, 172, 174, 176, 180, 184, 186, 188, 190, 196, 198, 200, 204, 207, 208
Offset: 1
Keywords
Examples
The positive divisors of 60 are 1,2,3,4,5,6,10,12,15,20,30,60. The divisor 4, a composite, is less than the prime divisor 5. So 60 is in this sequence.
Programs
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Maple
isA137428 := proc(n) local dvs,p,i ; dvs := sort(convert(numtheory[divisors](n) minus{1},list)) ; for i from 1 to nops(dvs) do if isprime(op(-i,dvs)) then p := op(-i,dvs) ; break ; fi ; od: for i from 1 to nops(dvs) do if op(i,dvs) < p and not isprime(op(i,dvs)) then RETURN(true) ; fi ; od: RETURN(false) ; end: for n from 1 to 400 do if isA137428(n) then printf("%d,",n) ; fi ; od: # R. J. Mathar, Apr 21 2008
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Mathematica
a = {}; For[n = 2, n < 300, n++, If[FactorInteger[n][[ -1, 1]] > Min[Select[ Divisors[n], ! PrimeQ[ # ]&& # > 1 &]], AppendTo[a, n]]]; a (* Stefan Steinerberger, Apr 21 2008 *) -
PARI
is(n)=#(n=factor(n)~)>1&&n[1,#n]>=n[1,1]*if(n[2,1]>1,n[1,1],n[1,2]) \\ M. F. Hasler, Jan 02 2015
Extensions
More terms from R. J. Mathar and Stefan Steinerberger, Apr 21 2008
Comments