A102619 - OEIS

%I #21 Sep 08 2022 08:45:16

%S 133,152,513,855,1064,1216,1729,1843,2071,2261,2413,2869,2926,3059,

%T 3439,3591,4104,4123,4921,4940,5833,6175,6840,7163,7657,8512,9386,

%U 9728,10773,13167,13357,13718,13832,13851,14174,14364,14744,15542,15561,16568

%N Numbers which are the sum of two positive cubes and divisible by 19.

%C 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

%H Vincenzo Librandi, <a href="/A102619/b102619.txt">Table of n, a(n) for n = 1..1000</a>

%t upto[n_] := Block[{t}, Union@ Reap[ Do[If[ Mod[t = x^3 + y^3, 19] == 0, Sow@t], {x, n^(1/3)}, {y, Min[x, (n - x^3)^(1/3)]}]][[2, 1]]]; upto[17000] (* _Giovanni Resta_, Jun 12 2020 *)

%o (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

%Y 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).

%K nonn,easy

%O 1,1

%A Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jan 31 2005