A102618 Numbers which are the sum of two positive cubes and divisible by 37.

370, 407, 1332, 2331, 2960, 3256, 4921, 5957, 8029, 8288, 9990, 10656, 10989, 12691, 12913, 13357, 13949, 14023, 14911, 16021, 16354, 17353, 18648, 18907, 19684, 19721, 20683, 22681, 23680, 24605, 24901, 26048, 27343, 30007, 30303, 32893, 34965, 35964, 36001, 36556, 37259, 39331, 39368, 39627

Offset: 1

Author

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

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003325. Other sequences of the form "sum of two positive cubes and divisible by ...": A224484, A224485, A101421, A101852, A094447, A099178, A102619, A101806, A224483, A102658.

Programs

Maple

N:= 200000: # for terms <= N
G:= expand(add(x^(i^3),i=1..floor(N^(1/3)))^2):
select(t -> coeff(G,x,t) > 0, [seq(i,i=37..N,37)]); # Robert Israel, Jun 12 2020

Mathematica

upto[n_] := Block[{t}, Union@ Reap[ Do[If[ Mod[t = x^3 + y^3, 37] == 0, Sow@ t], {x, n^(1/3)}, {y, Min[x, (n - x^3)^(1/3) ]}]][[2, 1]]]; upto[40000] (* Giovanni Resta, Jun 12 2020 *)
stpcQ[n_]:=Count[IntegerPartitions[n,{2}],?(AllTrue[CubeRoot[#],IntegerQ]&)]>0; Select[37* Range[1100],stpcQ] (* _Harvey P. Dale, Jul 10 2024 *)

Extensions

Corrected by Robert Israel, Jun 12 2020