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

1,1

Links

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

Mathematica

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

Prog

(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

Crossrefs

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

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

Sequence in context: A336360 A102750 A349810 * A349019 A225354 A166111

Adjacent sequences: A317089 A317090 A317091 * A317093 A317094 A317095

Keyword

nonn

Author

Gus Wiseman, Jul 21 2018

Status

approved