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

1,1

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A097318, A097319, A097320.

Sequence in context: A354922 A300080 A069169 * A231877 A080364 A325230

Adjacent sequences: A230763 A230764 A230765 * A230767 A230768 A230769

Keyword

nonn

Author

Alex Ratushnyak, Oct 29 2013

Status

approved