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

2, 6, 12, 18, 30, 60, 90, 150, 180, 210, 300, 360, 420, 450, 540, 600, 630, 1050, 1260, 1350, 1470, 1500, 2100, 2250, 2310, 2520, 2940, 3150, 3780, 4200, 4410, 4620, 5880, 6300, 6930, 7350, 8820, 9450, 10500, 11550, 12600, 13230, 13860, 14700, 15750, 16170

Offset: 1

Author

Gus Wiseman, Jul 21 2018

Keywords

• nonn

Examples

			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).
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A001222, A007916, A055932, A056239, A124010, A133808, A242414, A296150.

Cf. A317087, A317088, A317090, A317091, A317092.

Programs

Mathematica

normalQ[m_]:=Union[m]==Range[Max[m]];
Select[Range[10000],And[normalQ[PrimePi/@FactorInteger[#][[All,1]]],normalQ[FactorInteger[#][[All,2]]]]&]

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