cp's OEIS Frontend

A317089 Numbers whose prime factors span an initial interval of prime numbers and whose prime multiplicities span an initial interval of positive integers.

%I A317089 #8 Aug 26 2018 18:42:34
%S A317089 2,6,12,18,30,60,90,150,180,210,300,360,420,450,540,600,630,1050,1260,
%T A317089 1350,1470,1500,2100,2250,2310,2520,2940,3150,3780,4200,4410,4620,
%U A317089 5880,6300,6930,7350,8820,9450,10500,11550,12600,13230,13860,14700,15750,16170
%N A317089 Numbers whose prime factors span an initial interval of prime numbers and whose prime multiplicities span an initial interval of positive integers.
%H A317089 Andrew Howroyd, <a href="/A317089/b317089.txt">Table of n, a(n) for n = 1..300</a>
%e A317089 The sequence of rows of A296150 indexed by the terms of this sequence begins: (1), (21), (211), (221), (321), (3211), (3221), (3321), (32211), (4321), (33211), (322111), (43211).
%t A317089 normalQ[m_]:=Union[m]==Range[Max[m]];
%t A317089 Select[Range[10000],And[normalQ[PrimePi/@FactorInteger[#][[All,1]]],normalQ[FactorInteger[#][[All,2]]]]&]
%o A317089 (PARI) ok(n)={my(f=factor(n), p=f[,1], e=vecsort(f[,2],,8)); n > 1 && #p==primepi(p[#p]) && #e==e[#e]} \\ _Andrew Howroyd_, Aug 26 2018
%Y A317089 Cf. A001222, A007916, A055932, A056239, A124010, A133808, A242414, A296150.
%Y A317089 Cf. A317087, A317088, A317090, A317091, A317092.
%K A317089 nonn
%O A317089 1,1
%A A317089 _Gus Wiseman_, Jul 21 2018