login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A102618
Numbers which are the sum of two positive cubes and divisible by 37.
6
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
1,1
LINKS
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 *)
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.
Sequence in context: A224562 A276413 A161020 * A225104 A234985 A264895
KEYWORD
nonn
AUTHOR
Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jan 31 2005
EXTENSIONS
Corrected by Robert Israel, Jun 12 2020
STATUS
approved