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Search: id:A135718
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| A135718 |
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a(n) = smallest divisor of n^2 that is not a divisor of n. |
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1
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| 4, 9, 8, 25, 4, 49, 16, 27, 4, 121, 8, 169, 4, 9, 32, 289, 4, 361, 8, 9, 4, 529, 9, 125, 4, 81, 8, 841, 4, 961, 64, 9, 4, 25, 8, 1369, 4, 9, 16, 1681, 4, 1849, 8, 25, 4, 2209, 9, 343, 4, 9, 8, 2809, 4, 25, 16, 9, 4, 3481, 8
(list; graph; listen)
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OFFSET
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2,1
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FORMULA
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If n = product{p=primes, p|n} p^b(n,p), where each b(n,p) is a positive integer, then a(n) = the minimum value of a p^(b(n,p)+1) where p is a prime that divides n. Example: 24 has the prime factorization of 2^3 *3^1. So a(24) = the minimum of 2^(3+1) and 3^(1+1) = the minimum of 16 and 9, which is 9.
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EXAMPLE
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The divisors of 12 are 1,2,3,4,6,12. The divisors of 12^2 = 144 are 1,2,3,4,6,8,9,12,16,18,24,36,48,72,144. So the smallest divisor of 144 that is not a divisor of 12 is 8.
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MAPLE
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with(numtheory): a:=proc(n) options operator, arrow: op(1, `minus`(divisors(n^2), divisors(n))) end proc: seq(a(n), n=2..60); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 18 2008
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CROSSREFS
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Sequence in context: A085084 A075570 A133790 this_sequence A140580 A077662 A063718
Adjacent sequences: A135715 A135716 A135717 this_sequence A135719 A135720 A135721
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), May 10 2008
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 18 2008
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