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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 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

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