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

1,1

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.

Mathematica

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

Prog

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

Crossrefs

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

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

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

Subsequence of A337533.

Sequence in context: A345172 A212167 A339741 * A361393 A179983 A065872

Adjacent sequences: A317087 A317088 A317089 * A317091 A317092 A317093

Keyword

nonn

Author

Gus Wiseman, Jul 21 2018

Status

approved