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.

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.

Links

Table of n, a(n) for n=0..16.

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

Cf. A074111, A046099, A231122.

Essentially the same as A002110 and A121069.

Sequence in context: A054721 A374660 A074111 * A073087 A214822 A295497

Adjacent sequences: A231206 A231207 A231208 * A231210 A231211 A231212

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