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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Complement of A112769.
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..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
Sequence in context: A131881 A364728 A053460 * A316529 A329138 A334969
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 16 2018
STATUS
approved

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Last modified July 19 22:34 EDT 2024. Contains 374441 sequences. (Running on oeis4.)