A102619 Numbers which are the sum of two positive cubes and divisible by 19.

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

Offset: 1

Author

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

Keywords

• nonn
• easy

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

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).

Programs

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

Mathematica

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 *)