cp's OEIS Frontend

A137428 Positive integers n which have a composite divisor smaller than their largest prime factor.

%I A137428 #13 Jan 02 2015 10:18:33
%S A137428 20,28,40,42,44,52,56,60,66,68,76,78,80,84,88,92,99,100,102,104,110,
%T A137428 112,114,116,117,120,124,126,130,132,136,138,140,148,152,153,156,160,
%U A137428 164,168,170,171,172,174,176,180,184,186,188,190,196,198,200,204,207,208
%N A137428 Positive integers n which have a composite divisor smaller than their largest prime factor.
%C A137428 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
%e A137428 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.
%p A137428 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
%t A137428 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 *)
%o A137428 (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
%Y A137428 Cf. A006530, A088739.
%K A137428 nonn
%O A137428 1,1
%A A137428 _Leroy Quet_, Apr 17 2008
%E A137428 More terms from _R. J. Mathar_ and _Stefan Steinerberger_, Apr 21 2008