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

1,1

Links

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

Example

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).

Mathematica

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

Prog

(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

Crossrefs

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

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

Sequence in context: A113274 A181660 A036913 * A117311 A125024 A178480

Adjacent sequences: A317086 A317087 A317088 * A317090 A317091 A317092

Keyword

nonn

Author

Gus Wiseman, Jul 21 2018

Status

approved