A230766 - OEIS

%I #19 Feb 07 2025 19:25:11

%S 6,10,14,15,18,21,22,26,30,33,34,35,36,38,39,42,46,50,51,54,55,57,58,

%T 62,65,66,69,70,74,75,77,78,82,85,86,87,91,93,94,95,98,100,102,105,

%U 106,108,110,111,114,115,118,119,122,123,129,130,133,134,138,141

%N Numbers with more than one prime factor and, in the ordered factorization, the exponent never decreases when read from left to right.

%H Robert Israel, <a href="/A230766/b230766.txt">Table of n, a(n) for n = 1..10000</a>

%F If n = Product_{k=1..m} p(k)^e(k), then m > 1 and e(1) <= e(2) <= ... <= e(m).

%p filter:= proc(n) local F;

%p   F:= sort(ifactors(n)[2],(a,b) -> a[1] < b[1]);

%p   if nops(F) = 1 then return false fi;

%p   F:= F[..,2];

%p   F = sort(F)

%p end proc:

%p select(filter, [$2..200]); # _Robert Israel_, Feb 07 2025

%t fQ[n_] := Module[{f = Transpose[FactorInteger[n]][[2]]}, Length[f] > 1 && Min[Differences[f]] >= 0]; Select[Range[2, 200], fQ] (* _T. D. Noe_, Nov 04 2013 *)

%t Select[Range[150],PrimeNu[#]>1&&Min[Differences[FactorInteger[#][[All,2]]]]>=0&] (* _Harvey P. Dale_, May 22 2020 *)

%o (PARI) isok(n) = {my(f = factor(n), nbf = #f~); if (nbf < 2, return (0)); lastexp = 0; for (i=1, nbf, if ((newexp = f[i, 2]) < lastexp, return (0)); lastexp = newexp;); return (1);} \\ _Michel Marcus_, Oct 30 2013

%Y Cf. A097318, A097319, A097320.

%K nonn

%O 1,1

%A _Alex Ratushnyak_, Oct 29 2013