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

1,1

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

Links

Table of n, a(n) for n=1..56.

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

Cf. A006530, A088739.

Sequence in context: A139805 A141823 A367632 * A368089 A367455 A350841

Adjacent sequences: A137425 A137426 A137427 * A137429 A137430 A137431

Keyword

nonn

Author

Leroy Quet, Apr 17 2008

Extensions

More terms from R. J. Mathar and Stefan Steinerberger, Apr 21 2008

Status

approved