A185681 a(n) = start of n consecutive numbers divisible respectively by prime(k)^n, for k=1..n.

2, 8, 21248, 1197741248, 16414088688381248, 579329868703698452660781248, 20182773361697812807734811854155781248, 28343998868273668587268878406666355122557128720825781248

Offset

1,1

Comments

a(n) is the smallest number such that: prime(1)^n | a(n), prime(2)^n | a(n)+1,..., prime(n)^n | a(n)+n-1.

Links

Table of n, a(n) for n=1..8.

Example

a(1) = 2 as 2 is divisible by 2^1 ;
a(2) = 8 as 8 and 9 are divisible by 2^2 and 3^2 respectively ;
a(3) = 21248 as 21248, 21249 and 21250 are divisible by 2^3, 3^3 and 5^3 respectively.

Mathematica

Table[ ChineseRemainder[ Table[ -i, {i, 0, n - 1}], Table[ Prime[i]^n, {i,  1, n}]], {n, 2, 10}]

Crossrefs

Cf. A069561, A072562, A181682.

Sequence in context: A038582 A309860 A058437 * A046967 A007753 A272331

Adjacent sequences: A185678 A185679 A185680 * A185682 A185683 A185684

Keyword

nonn

Author

Michel Lagneau, Feb 10 2011

Status

approved