A248331 a(n) is the first term in a length n sequence of consecutive integers that are divisible respectively by the square of the first n primes.

0, 8, 548, 29348, 1308248, 652312448, 180110691548, 65335225716548, 38733853511213648, 4368761145612023948, 1804216772228848838648, 14884872991210984993091648, 9816873967836575781598117448, 143397994078495393809327283088348

Offset

1,2

Comments

The sequence of consecutive integers is the smallest such sequence.

References

K. H. Rosen, Elementary Number Theory and its Applications, Addison-Wesley, 1984, page 113.

Links

Table of n, a(n) for n=1..14.

Example

a(4)=29348.  29348 is divisible by 4, 29349 is divisible by 9, 29350 is divisible by 25, 29351 is divisible by 49.
The first few rows of the triangle of quotients are:
0;
2, 1;
137, 61, 22;
7337, 3261, 1174, 599;
327062, 145361, 52330, 26699, 10812;
163078112, 72479161, 26092498, 13312499, 5391012, 3859837;
- Michel Marcus, Oct 27 2014

Mathematica

Table[ChineseRemainder[Reverse[Range[-k, 0]], Table[Prime[n]^2, {n, 1, k + 1}]], {k, 0, 13}]

Crossrefs

Cf. A069561.

Sequence in context: A334255 A174252 A181682 * A301950 A240300 A240432

Adjacent sequences: A248328 A248329 A248330 * A248332 A248333 A248334

Keyword

nonn

Author

Geoffrey Critzer, Oct 26 2014

Status

approved