A224484 -id:A224484 - cp's OEIS frontend

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

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

nonn

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

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.

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

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 *)

Corrected by Robert Israel, Jun 12 2020

A224485 Numbers which are the sum of two positive cubes and divisible by 5.

Original entry on oeis.org

35, 65, 250, 280, 370, 520, 730, 855, 945, 1125, 1395, 1755, 2000, 2060, 2205, 2240, 2540, 2745, 2960, 3500, 3925, 4075, 4160, 4375, 4825, 4940, 5425, 5840, 6175, 6750, 6840, 6860, 7075, 7110, 7560, 8125, 8190, 9000, 9325, 9990

Offset: 1

Vincenzo Librandi, May 10 2013

If 12*h-75 is a square then some values of 5*h are in this sequence. It is easy to verify that h is of the form 3*m^2-3*m+7, and therefore 5*(3*m^2-3*m+7) = (3-m)^3+(m+2)^3.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A224484 (divisible by k=3), A101421 (k=7), A101852 (k=11), A094447 (k=13), A099178 (k=17), A102619 (k=19), A101806 (k=23), A224483 (k=29), A102658 (k=31), A102618 (k=37).

upto[n_] := Block[{t}, Union@ Reap[ Do[If[Mod[t = x^3 + y^3, 5] == 0, Sow@t], {x, n^(1/3)}, {y, Min[x, (n - x^3)^(1/3)]}]][[2, 1]]]; upto[10000] (* Giovanni Resta, Jun 12 2020 *)

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

Extensions