A230766 Numbers with more than one prime factor and, in the ordered factorization, the exponent never decreases when read from left to right.

6, 10, 14, 15, 18, 21, 22, 26, 30, 33, 34, 35, 36, 38, 39, 42, 46, 50, 51, 54, 55, 57, 58, 62, 65, 66, 69, 70, 74, 75, 77, 78, 82, 85, 86, 87, 91, 93, 94, 95, 98, 100, 102, 105, 106, 108, 110, 111, 114, 115, 118, 119, 122, 123, 129, 130, 133, 134, 138, 141

Offset: 1

Author

Alex Ratushnyak, Oct 29 2013

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A097318, A097319, A097320.

Programs

Maple

filter:= proc(n) local F;
  F:= sort(ifactors(n)[2],(a,b) -> a[1] < b[1]);
  if nops(F) = 1 then return false fi;
  F:= F[..,2];
  F = sort(F)
end proc:
select(filter, [$2..200]); # Robert Israel, Feb 07 2025

Mathematica

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

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

Formula

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