A323056 Numbers with exactly five distinct exponents in their prime factorization, or five distinct parts in their prime signature.

174636000, 206388000, 244490400, 261954000, 269892000, 274428000, 288943200, 291060000, 301644000, 309582000, 343980000, 349272000, 365148000, 366735600, 377848800, 383292000, 404838000, 411642000, 412776000, 422301600, 433414800, 449820000, 452466000, 457380000

Offset: 1

Author

Gus Wiseman, Jan 03 2019

Keywords

• nonn

Comments

The first term is A006939(5) = 174636000.

Positions of 5's in A071625.

Numbers k such that A001221(A181819(k)) = 5.

Examples

			174636000 = 2^5 * 3^4 * 5^3 * 7^2 * 11^1 has five distinct exponents so belongs to the sequence.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

One distinct exponent: A062770 or A072774.

Two distinct exponents: A323055.

Three distinct exponents: A323024.

Four distinct exponents: A323025.

Five distinct exponents: A323056.

Cf. A001221, A001222, A006939, A051270, A059404, A071625, A118914, A181819, A182855, A323014, A323022, A323024.

Programs

Mathematica

Select[Range[300000000],Length[Union[Last/@FactorInteger[#]]]==5&]

PARI

is(n) = #Set(factor(n)[, 2]) == 5 \\ David A. Corneth, Jan 12 2019

Extensions

a(13)-a(24) from Daniel Suteu, Jan 12 2019