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A164798
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a(n) = the smallest integer >= n such that a(n)!/(n-1)! is divisible by every prime from 2 to the largest prime divisor of a(n)!/(n-1)!. (a(1)=1.)
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3
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1, 2, 4, 4, 6, 6, 10, 8, 10, 14, 15, 12, 22, 15, 16, 16, 26, 18, 34, 21, 38, 38, 38, 24, 46, 46, 46, 46, 46, 30, 58, 32, 62, 62, 36, 36, 62, 74, 74, 74, 74, 82, 82, 86, 86, 86, 86, 48, 94, 94, 94, 94, 94, 54, 106, 106, 106, 106, 106, 60, 118, 122, 66, 64, 122, 122, 122, 134
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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Consider the products of consecutive integers, m!/9!, m >= 10. First, 10 is divisible by 2 and 5, but there is a prime gap since 3 is missing from the factorization. 10*11 is divisible by 2, 5, and 11, but 3 and 7 are missing. 10*11*12 is divisible by 2, 3, 5, and 11, but 7 is missing. 10*11*12*13 is divisible by all primes up to 13, except 7. But 10*11*12*13*14 is indeed divisible by every prime from 2 to 13. So a(10) = 14.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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