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A102619
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Numbers which are the sum of two positive cubes and divisible by 19.
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5
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133, 152, 513, 855, 1064, 1216, 1729, 1843, 2071, 2261, 2413, 2869, 2926, 3059, 3439, 3591, 4104, 4123, 4921, 4940, 5833, 6175, 6840, 7163, 7657, 8512, 9386, 9728, 10773, 13167, 13357, 13718, 13832, 13851, 14174, 14364, 14744, 15542, 15561, 16568
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OFFSET
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1,1
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COMMENTS
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If 12*h-1083 is a square then some values of 19*h are in this sequence. It is easy to verify that h is of the form 3*m^2-3*m+91, and therefore 19*(3*m^2-3*m+91) = (10-m)^3+(m+9)^3. - Vincenzo Librandi, May 10 2013
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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MATHEMATICA
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Select[Union[Total/@(Tuples[Range[40], 2]^3)], Divisible[#, 19]&] (* Vincenzo Librandi, Mat 08 2013 *)
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PROG
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(MAGMA) [n: n in [2..2*10^4] | exists{i: i in [1..Iroot(n-1, 3)] | IsPower(n-i^3, 3) and IsZero(n mod 19)}]; // Bruno Berselli, May 10 2013
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CROSSREFS
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Cf. A003325, A101421 (divisible by k=7), A101852 (k=11), A094447 (k=13), A099178 (k=17), A101806 (k=23), A224483 (k=29), A102658 (k=31), A102618 (k=37).
Sequence in context: A003915 A046439 A031188 * A020446 A123997 A050882
Adjacent sequences: A102616 A102617 A102618 * A102620 A102621 A102622
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KEYWORD
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nonn,easy,changed
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AUTHOR
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Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jan 31 2005
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STATUS
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approved
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