A317090 Positive integers whose prime multiplicities span an initial interval of positive integers.

2, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85

Offset: 1

Author

Gus Wiseman, Jul 21 2018

Keywords

• nonn

Comments

The first term in this sequence but absent from A179983 is 180.

The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 6, 78, 820, 8379, 84440, 846646, 8473868, 84763404, 847714834, 8477408261, ... . Apparently, the asymptotic density of this sequence exists and equals 0.8477... . - Amiram Eldar, Aug 04 2024

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index to sequences related to prime signature.

Crossrefs

Cf. A001222, A007916, A055932, A056239, A069799, A112798, A124010, A133808.

Cf. A317087, A317088, A317089, A317091, A317092.

Subsequences: A129912\{1}, A179983\{1}.

Subsequence of A337533.

Programs

Mathematica

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

PARI

is(k) = {my(e = Set(factor(k)[,2])); k > 1 && vecmax(e) == #e;} \\ Amiram Eldar, Aug 04 2024