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A093195
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Least number which is the sum of two distinct nonzero squares in exactly n ways.
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5
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5, 65, 325, 1105, 8125, 5525, 105625, 27625, 71825, 138125, 126953125, 160225, 1221025, 3453125, 1795625, 801125, 446265625, 2082925, 41259765625, 4005625, 44890625, 30525625, 30994415283203125, 5928325, 303460625, 53955078125, 35409725, 100140625
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| Ray Chandler, Table of n, a(n) for n = 1..1438 (a(1439) exceeds 1000 digits).
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FORMULA
| An algorithm to compute the n-th term of this sequence: Write each of 2n and 2n+1 as products of their divisors in all possible ways and in decreasing order. For each product, equate each divisor in the product to (a1+1)(a2+1)...(ar+1), so that a1>=a2>=a3>=...>=ar, and solve for the ai. Evaluate A002144(1)^a1 x A002144(2)^a2 x ... x A002144(r)^ar for each set of values determined above, then the smaller of these products is the least integer to have precisely n partitions into a sum of two distinct positive squares. [From Ant King (mathstutoring(AT)ntlworld.com), Dec 14 2009; May 26 2010]
a(n) = min(A018782(2n),A018782(2n+1)).
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CROSSREFS
| Cf. A002144, A018782, A054994, A025302-A025311 (first entries). See A016032, A000446 and A124980 for other versions.
Sequence in context: A091105 A071902 A052199 * A195579 A061184 A118004
Adjacent sequences: A093192 A093193 A093194 * A093196 A093197 A093198
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KEYWORD
| nonn
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AUTHOR
| Lekraj Beedassy (blekraj(AT)yahoo.com), Apr 22 2004
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EXTENSIONS
| More terms from Ant King (mathstutoring(AT)ntlworld.com), Dec 14 2009 and Feb 07 2010
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