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

1,2

Comments

Complement of A112769.

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A131881 A364728 A053460 * A316529 A329138 A334969

Adjacent sequences: A304675 A304676 A304677 * A304679 A304680 A304681

Keyword

nonn

Author

Gus Wiseman, May 16 2018

Status

approved