

A304678


Numbers with weakly increasing prime multiplicities.


31



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
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OFFSET

1,2


COMMENTS



LINKS



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..t1]))(nops(l)))(sort(ifactors(n)[2])):


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.


KEYWORD

nonn


AUTHOR



STATUS

approved



