A061236 Smallest number with p(n)^3 divisors where p(n) is n-th prime.

24, 900, 810000, 729000000, 590490000000000, 531441000000000000, 430467210000000000000000, 387420489000000000000000000, 313810596090000000000000000000000

Offset

1,1

Links

Table of n, a(n) for n=1..9.

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)=n-th 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: A107391 A281778 A006147 * A266997 A359644 A001784

Adjacent sequences: A061233 A061234 A061235 * A061237 A061238 A061239

Keyword

nonn

Author

Labos Elemer, Jun 01 2001

Status

approved