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A137428
Positive integers n which have a composite divisor smaller than their largest prime factor.
3
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
1,1
COMMENTS
The primitive elements of this sequence are those of the form s*p, where s is a semiprime and p a prime larger than s, cf. A252478. Any multiple of these primitive terms is also in the sequence. - M. F. Hasler, Jan 02 2015
EXAMPLE
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.
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
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 *)
PROG
(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
CROSSREFS
Sequence in context: A139805 A141823 A367632 * A368089 A367455 A350841
KEYWORD
nonn
AUTHOR
Leroy Quet, Apr 17 2008
EXTENSIONS
More terms from R. J. Mathar and Stefan Steinerberger, Apr 21 2008
STATUS
approved