A323056 - OEIS

%I #18 Feb 17 2019 20:40:29

%S 174636000,206388000,244490400,261954000,269892000,274428000,

%T 288943200,291060000,301644000,309582000,343980000,349272000,

%U 365148000,366735600,377848800,383292000,404838000,411642000,412776000,422301600,433414800,449820000,452466000,457380000

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

%C The first term is A006939(5) = 174636000.

%C Positions of 5's in A071625.

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

%H David A. Corneth, <a href="/A323056/b323056.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%o (PARI) is(n) = #Set(factor(n)[, 2]) == 5 \\ _David A. Corneth_, Jan 12 2019

%Y One distinct exponent: A062770 or A072774.

%Y Two distinct exponents: A323055.

%Y Three distinct exponents: A323024.

%Y Four distinct exponents: A323025.

%Y Five distinct exponents: A323056.

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

%K nonn

%O 1,1

%A _Gus Wiseman_, Jan 03 2019

%E a(13)-a(24) from _Daniel Suteu_, Jan 12 2019