The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A253296 Numbers with more composite divisors than prime divisors such that all the prime divisors are smaller than the composite divisors. 0
 8, 12, 16, 18, 24, 27, 30, 32, 36, 45, 48, 50, 54, 63, 64, 70, 72, 75, 81, 90, 96, 98, 105, 108, 125, 128, 135, 144, 147, 150, 154, 162, 165, 175, 182, 189, 192, 195, 216, 225, 231, 242, 243, 245, 250, 256, 270, 273, 275, 286, 288, 315, 324, 325, 338, 343, 350 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS List of composite numbers with n >= 2 nontrivial divisors where the k smallest nontrivial divisors are all primes and the n - k largest nontrivial divisors are all nonprimes, 1 <= k < n. Here the term "nontrivial divisors" only serves to exclude 1. Except for semiprimes, all composite numbers have more composite divisors than prime divisors. - Robert G. Wilson v, Jan 12 2015 LINKS EXAMPLE 36 is in the sequence because its nontrivial divisors are 2, 3, 4, 6, 9, 12, 18, and of these, the first two are prime and the rest are composite. 40 is not in the sequence because its nontrivial divisors are 2, 4, 5, 8, 10, 20, and the composite divisor 4 falling between the prime divisors 2 and 5 disqualifies 40 from membership in the sequence. MAPLE filter:= proc(n) local f, x; f:= ifactors(n)[2]; if mul(t[2]+1, t=f) <= 2*nops(f)+1 then return false fi; if f[1, 2] > 1 then x:= f[1, 1]^2 else x:= f[1, 1]*f[2, 1] fi; max(seq(t[1], t=f)) < x end proc: select(filter, [\$1..1000]); # Robert Israel, Jan 01 2015 MATHEMATICA ntd[n_] := (dlist = Divisors[n]; dlist[[2 ;; Length[dlist] - 1]]) test[n_] := (tlist = ntd[n];   If[tlist == {}, False,    index = 1;    While[index <= Length[tlist] && PrimeQ[tlist[[index]]] == True,     index = index + 1];    If[index == 1 || index > Length[tlist], False,     While[index <= Length[tlist] && PrimeQ[tlist[[index]]] == False,      index = index + 1];     If[index <= Length[tlist], False, True]]]) Select[Table[n, {n, 2, 2500, 1}], test] (* Savoric *) primeDivs[n_Integer] := Select[Divisors[n], PrimeQ]; compDivs[n_Integer] := Drop[Complement[Divisors[n], primeDivs[n]], 1]; Select[Range[4, 500], Not[PrimeQ[#]] && primeDivs[#][[-1]] < compDivs[#][[1]] && Length[primeDivs[#]] < Length[compDivs[#]] &] (* Alonso del Arte, Dec 31 2014 *) fQ[n_] := Block[{d = PrimeQ@ Most@ Rest@ Divisors@ n}, d[[1]] == True && d[[-1]] == False && Length@ Split@ d == 2]; Select[ Range@ 350, fQ] (* Robert G. Wilson v, Jan 12 2015 *) CROSSREFS Cf. A137428. Sequence in context: A083348 A174261 A063539 * A081925 A049199 A337806 Adjacent sequences:  A253293 A253294 A253295 * A253297 A253298 A253299 KEYWORD nonn AUTHOR Michael Savoric, Dec 30 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 21 01:46 EDT 2021. Contains 347596 sequences. (Running on oeis4.)