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A067721
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Least number k such that k (k + n) is a perfect square, or 0 if impossible.
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7
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1, 0, 0, 1, 0, 4, 2, 9, 1, 3, 8, 25, 4, 36, 18, 1, 2, 64, 6, 81, 16, 4, 50, 121, 1, 20, 72, 9, 36, 196, 2, 225, 4, 11, 128, 1, 12, 324, 162, 13, 5, 400, 8, 441, 100, 3, 242, 529, 1, 63, 40, 17, 144, 676, 18, 9, 7, 19, 392, 841, 4, 900, 450, 1, 8, 16, 22, 1089, 256, 23, 2, 1225
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| Impossible only for 1, 2 and 4. k equals 1 when n is in A005563. k equals 2 when n is in A054000.
Let k*(k+n)= c*c, gcd(n,k,c)=1 . Then primitive triples (n,k,c) are of the form : 1) n is prime. (n,k,c)=( p, (p*p-2*p+1)/4, (p*p-1)/4 ) 2) n=(c/t)*(c/t)- t*t, n is not a prime, t positive integer. (n,k,c)=( (c/t)*(c/t)- t*t, t*t, c ) [From Ctibor O. Zizka (c.zizka(AT)email.cz), May 04 2009]
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LINKS
| Carmine Suriano, Table of n, a(n) for n = 0..2000
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EXAMPLE
| a(7) = 9 because 9 (7+9) = 144 = 12^2.
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MATHEMATICA
| Do[k = 1; While[ !IntegerQ[ Sqrt[ k (k + n)]], k++ ]; Print[k], {n, 5, 75} ]
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CROSSREFS
| Cf. A067632, A007913, A076942.
Sequence in context: A127470 A199449 A010649 * A159899 A201531 A021237
Adjacent sequences: A067718 A067719 A067720 * A067722 A067723 A067724
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 05 2002
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