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 A102619 Numbers which are the sum of two positive cubes and divisible by 19. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 MATHEMATICA Select[Union[Total/@(Tuples[Range[40], 2]^3)], Divisible[#, 19]&] (* Vincenzo Librandi, Mat 08 2013 *) PROG (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 CROSSREFS 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 KEYWORD nonn,easy,changed AUTHOR Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jan 31 2005 STATUS approved

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