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A248331
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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.
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0
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0, 8, 548, 29348, 1308248, 652312448, 180110691548, 65335225716548, 38733853511213648, 4368761145612023948, 1804216772228848838648, 14884872991210984993091648, 9816873967836575781598117448, 143397994078495393809327283088348
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OFFSET
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1,2
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COMMENTS
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The sequence of consecutive integers is the smallest such sequence.
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REFERENCES
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K. H. Rosen, Elementary Number Theory and its Applications, Addison-Wesley, 1984, page 113.
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LINKS
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EXAMPLE
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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;
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MATHEMATICA
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Table[ChineseRemainder[Reverse[Range[-k, 0]], Table[Prime[n]^2, {n, 1, k + 1}]], {k, 0, 13}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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