A304678 Numbers with weakly increasing prime multiplicities.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 49, 50, 51, 53, 54, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 75, 77, 78, 79, 81, 82, 83

Offset: 1

Author

Gus Wiseman, May 16 2018

Keywords

• nonn

Comments

Complement of A112769.

Examples

			12 = 2*2*3 has prime multiplicities (2,1) so is not in the sequence.
36 = 2*2*3*3 has prime multiplicities (2,2) so is in the sequence.
150 = 2*3*5*5 has prime multiplicities (1,1,2) so is in the sequence.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A001222, A071365, A112769, A130091, A133808, A133811, A242031, A304465, A304679, A304687.

Programs

Maple

q:= n-> (l-> (t-> andmap(i-> l[i, 2]<=l[i+1, 2],
        [$1..t-1]))(nops(l)))(sort(ifactors(n)[2])):
select(q, [$1..120])[];  # Alois P. Heinz, Nov 11 2019

Mathematica

Select[Range[200],OrderedQ[FactorInteger[#][[All,2]]]&]
Select[Range[90],Min[Differences[FactorInteger[#][[;;,2]]]]>=0&] (* Harvey P. Dale, Jan 28 2024 *)

PARI

isok(n) = my(vm = factor(n)[,2]); vm == vecsort(vm); \\ Michel Marcus, May 17 2018