A248331 - OEIS

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.

%I #24 Oct 29 2014 04:18:26

%S 0,8,548,29348,1308248,652312448,180110691548,65335225716548,

%T 38733853511213648,4368761145612023948,1804216772228848838648,

%U 14884872991210984993091648,9816873967836575781598117448,143397994078495393809327283088348

%N 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.

%C The sequence of consecutive integers is the smallest such sequence.

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

%e a(4)=29348. 29348 is divisible by 4, 29349 is divisible by 9, 29350 is divisible by 25, 29351 is divisible by 49.

%e The first few rows of the triangle of quotients are:

%e 0;

%e 2, 1;

%e 137, 61, 22;

%e 7337, 3261, 1174, 599;

%e 327062, 145361, 52330, 26699, 10812;

%e 163078112, 72479161, 26092498, 13312499, 5391012, 3859837;

%e - _Michel Marcus_, Oct 27 2014

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

%Y Cf. A069561.

%K nonn

%O 1,2

%A _Geoffrey Critzer_, Oct 26 2014