login
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.
2
1, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810, 304250263527210, 13082761331670030, 614889782588491410, 32589158477190044730, 1922760350154212639070
OFFSET
0,2
COMMENTS
Primorial numbers without 2.
EXAMPLE
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;
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;
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;
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.
CROSSREFS
Essentially the same as A002110 and A121069.
Sequence in context: A054721 A374660 A074111 * A073087 A214822 A295497
KEYWORD
nonn,less
AUTHOR
Gerasimov Sergey, Nov 05 2013
EXTENSIONS
Offset corrected by Peter Munn, Jan 03 2023
Name corrected by Peter Munn, Oct 04 2024
STATUS
approved