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A317089
Numbers whose prime factors span an initial interval of prime numbers and whose prime multiplicities span an initial interval of positive integers.
19
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
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 21 2018
STATUS
approved