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Search: id:A024606
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| A024606 |
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Numbers expressible in more than one way as i^2 - i*j + j^2, where 1 <= i <= j. |
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3
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| 7, 13, 19, 21, 28, 31, 37, 39, 43, 49, 52, 57, 61, 63, 67, 73, 76, 79, 84, 91, 93, 97, 103, 109, 111, 112, 117, 124, 127, 129, 133, 139, 147, 148, 151, 156, 157, 163, 169, 171, 172, 175, 181, 183, 189, 193, 196, 199, 201, 208, 211, 217, 219, 223, 228, 229, 237, 241, 244, 247
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Alternatively, numbers expressible in more than one way as i^2 - i*j + j^2, where 1 <= i < j. The following argument shows that the two definitions are equivalent. Note first that i^2-i*j+j^2 = (j-i)^2-(j-i)*j+j^2, so the only non-duplicated values i^2-i*j+j^2 with 1<=i<j are when j=2*i, whence i^2-i*j+j^2 = 3i^2. On the other hand, the values with i=j are j^2. There are no integer solutions to 3i^2 = j^2 with i>=1. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 03 2006
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FORMULA
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Numbers expressible as i^2+i*j+j^2 with 1<=i<j. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 03 2006
Numbers whose prime factorization contains at least one prime congruent to 1 mod 6 and any prime factor congruent to 2 mod 3 has even multiplicity. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 03 2006
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CROSSREFS
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Cf. A118886.
Sequence in context: A107744 A160007 A024613 this_sequence A074628 A031194 A121058
Adjacent sequences: A024603 A024604 A024605 this_sequence A024607 A024608 A024609
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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