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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
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 16 2018
STATUS
approved