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A024670
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Numbers that are sums of 2 distinct positive cubes.
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23
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9, 28, 35, 65, 72, 91, 126, 133, 152, 189, 217, 224, 243, 280, 341, 344, 351, 370, 407, 468, 513, 520, 539, 559, 576, 637, 728, 730, 737, 756, 793, 854, 855, 945, 1001, 1008, 1027, 1064, 1072, 1125, 1216, 1241, 1332, 1339, 1343, 1358, 1395, 1456, 1512, 1547, 1674
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This sequence contains no primes since x^3+y^3=(x^2-x*y+y^2)*(x+y). - M. F. Hasler, Apr 12 2008
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LINKS
| M. F. Hasler, Table of n, a(n) for n=1,...,902.
Index to sequences related to sums of cubes
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EXAMPLE
| 9 is in the sequence since 2^3 + 1^3 = 9.
35 is in the sequence since 3^3 + 2^3 = 35.
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MATHEMATICA
| lst={}; Do[Do[x=a^3; Do[y=b^3; If[x+y==n, AppendTo[lst, n]], {b, Floor[(n-x)^(1/3)], a+1, -1}], {a, Floor[n^(1/3)], 1, -1}], {n, 6!}]; lst (* From Vladimir Orlovsky, Jan 22 2009 *)
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PROG
| (PARI) isA024670(n)=for( i=ceil(sqrtn( n\2+1, 3)), sqrtn(n-.5, 3), isA000578(n-i^3) & return(1)) /* One could also use "for( i=2, sqrtn( n\2-1, 3), ...)" but this is much slower since there are less cubes in [n/2, n] than in [1, n/2]. Replacing the -1 here by +.5 would yield A003325, allowing for a(n)=x^3+x^3. Replacing -1 by 0 may miss some a(n) of this form due to rounding errors. */ - M. F. Hasler, Apr 12 2008
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CROSSREFS
| See also: Sums of 2 positive cubes (not necessarily distinct): A003325. Sums of 3 distinct positive cubes: A024975. Sums of distinct positive cubes: A003997. Sums of 2 distinct nonnegative cubes: A114090. Sums of 2 nonnegative cubes: A004999. Sums of 2 distinct positive squares: A004431. Cubes: A000578.
Sequence in context: A044999 A155473 A127629 * A141805 A124360 A041152
Adjacent sequences: A024667 A024668 A024669 * A024671 A024672 A024673
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| Name edited by Zak Seidov (zakseidov(AT)yahoo.com), May 31 2011
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