cp's OEIS Frontend

A231209 Smallest squarefree number k with 2^n ways to write k as k = x*y, where x, y = squarefree numbers, 1 <= x <= y <= k.

%I A231209 #30 Oct 05 2024 09:41:07
%S A231209 1,6,30,210,2310,30030,510510,9699690,223092870,6469693230,
%T A231209 200560490130,7420738134810,304250263527210,13082761331670030,
%U A231209 614889782588491410,32589158477190044730,1922760350154212639070
%N A231209 Smallest squarefree number k with 2^n ways to write k as k = x*y, where x, y = squarefree numbers, 1 <= x <= y <= k.
%C A231209 Primorial numbers without 2.
%e A231209 a(0)=1 because squarefree number k=1 with 2^0=1 way to write k = x*y = 1*1 where x=1 and y=1 are squarefree numbers;
%e A231209 a(1)=6 because squarefree number k=6 with 2^1=2 ways to write k = x*y = 1*6 = 2*3 where 1, 6, 2, 3, are all squarefree numbers;
%e A231209 a(2)=30 because squarefree number k=30 with 2^2=4 ways to write k = 1*30 = 2*15 = 3*10 = 5*6 where 1, 30, 2, 15, 3, 10, 5, 6 are all squarefree numbers;
%e A231209 a(3)=210 because squarefree number k=210 with 2^3=8 ways to write k = 1*210 = 2*105 = 3*70 = 5*42 = 6*35 = 7*30 = 10*21 = 14*15 where 1, 210, 2, 105, 3, 70, 5, 42, 6, 35, 7, 30, 10, 21, 14, 15 are all squarefree numbers.
%Y A231209 Cf. A074111, A046099, A231122.
%Y A231209 Essentially the same as A002110 and A121069.
%K A231209 nonn,less
%O A231209 0,2
%A A231209 _Gerasimov Sergey_, Nov 05 2013
%E A231209 Offset corrected by _Peter Munn_, Jan 03 2023
%E A231209 Name corrected by _Peter Munn_, Oct 04 2024