A317092 Positive integers whose prime multiplicities are weakly decreasing and span an initial interval of positive integers.

2, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 89, 91, 92

Offset: 1

Author

Gus Wiseman, Jul 21 2018

Keywords

• nonn

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..25000

Crossrefs

Cf. A001222, A007916, A055932, A056239, A112798, A124010, A133808, A242031.

Cf. A317087, A317088, A317089, A317090, A317091.

Programs

Mathematica

normalQ[m_]:=Union[m]==Range[Max[m]];
Select[Range[2,100],And[normalQ[FactorInteger[#][[All,2]]],OrderedQ[Reverse[FactorInteger[#][[All,2]]]]]&]

PARI

is(n) = my (f=factor(n), w=#f~); if (w==0 || f[w,2]!=1, return (0), for (k=1, w-1, if (f[k,2]!=f[k+1,2] && f[k,2]!=1+f[k+1,2], return (0))); return (1)) \\ Rémy Sigrist, Sep 05 2018