|
| |
|
|
A061236
|
|
Smallest number with p(n)^3 divisors where p(n) is n-th prime.
|
|
0
| |
|
|
24, 900, 810000, 729000000, 590490000000000, 531441000000000000, 430467210000000000000000, 387420489000000000000000000, 313810596090000000000000000000000
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
FORMULA
| For p=2, 24 is the solution. If p>2 prime, then suitable powers of 30 are the least solutions: a(n)=Min{x|d(x)=A000005(x)=p(n)^3}=30^[p(n)-1], p(n)=nth prime; d[2^(ppp-1)]=d[2^(pp-1)3^(p-1)]=d[30^(p-1)]=p^3 and 2^(ppp-1)>2^(pp-1)3^(p-1)>30^(p-1) holds if p>2.
|
|
|
EXAMPLE
| p=2, then d(128)=d(24)=d(30)=8 and a(1)=24<30 is the smallest; P=5, then 2^124>(2^24)*(3^4)>30^4=810000=a(3).
|
|
|
CROSSREFS
| Cf. A000005, A005179, A003680, A037992, A061283, A061286, A061148, A061149.
Sequence in context: A160111 A107391 A006147 * A001784 A172206 A001866
Adjacent sequences: A061233 A061234 A061235 * A061237 A061238 A061239
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jun 01 2001
|
| |
|
|
