This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(2) = 5972 = 1222 + 4750 = 1925 + 4047.
a(2) = 1729 = 1^3 + 12^3 = 9^3 + 10^3. a(3) = 1009 = 1^3 + 2^3 + 10^3 = 4^3 + 6^3 + 9^3.
G:= mul(1+t*x^(i^3), i=1..35): R:= -1: for m from 2 do C:= expand(coeff(G,t,m)): C2:= convert(select(s -> subs(x=1,s)=2, C),list); v:= min(map(degree,C2)); if v >= 36^3 + add(i^3,i=1..m-1) then break fi; R:= R,v; od: R; # Robert Israel, Jul 08 2024
1729Range[0, 37] (* Alonso del Arte, Feb 19 2015 *)
a(n)=1729*n \\ Charles R Greathouse IV, Feb 21 2015
concat(0, Vec(1729*x/(1-x)^2 + O(x^40))) \\ Elmo R. Oliveira, Jun 23 2025
1729^Range[0, 9] (* Alonso del Arte, Oct 18 2014 *)
a(n)=1729^n \\ Charles R Greathouse IV, Jan 20 2014
f[n_] := PrimeOmega@ n == 2; lst = {}; Do[Do[Do[If[And[f[a], f[b], f[c], f[p = a^3 + b^3 + c^3]], AppendTo[lst, p]], {c, b - 1, 1, -1}], {b, a - 1, 1, -1}], {a, 200}]; lst1 = Sort@ lst; lst = {}; Do[If[lst1[[n]] == lst1[[n + 1]], AppendTo[lst, lst1[[n]]]], {n, Length[lst1] - 1}]; lst (* Corrected by Michael De Vlieger, May 21 2017 *)
a(0) = 4 because the smallest number that cannot be represented as a sum of 3 nonnegative cubes is 4. a(1) = 0 is the sum of three 0's. a(2) = 216 = 3^3 + 4^3 + 5^3 = 6^3 + 0 + 0. a(3) = 5104 = 1 + 12^3 + 15^3 = 2^3 + 10^3 + 16^3 = 9^3 + 10^3 + 15^3.
TOP = 6000000
a = [0]*TOP
for b in range(TOP):
b3 = b**3
if b3*3>=TOP: break
for c in range(b,TOP):
c3 = b3 + c**3
if c3>=TOP: break
for d in range(c,TOP):
res = c3 + d**3
if res>=TOP: break
a[res] += 1
m = max(a)
r = [-1] * (m+1)
for i in range(TOP):
if r[a[i]]==-1: r[a[i]]=i
print(r)
a(3) * a(26) = 3 * 576 = 1728. a(4) * a(25) = 4 * 432 = 1728. a(5) * a(24) = 6 * 288 = 1728.
Divisors[1728]
divisors(1728)
divisors(1728);
a(1) = 7859 = 10^3+19^3; a(2) = 681179092750 = 4365^3+8425^3 = 5275^3+8115^3; a(3) = 4466203788801326865111 = 6193863^3+16170804^3 = 8456292^3+15688647^3 = 9457695^3+15354846^3.
a(1) = A006530(A001235(1)) = A006530(1729) = 19.
FactorInteger[Select[Range[2*10^5], Length[PowersRepresentations[#, 2, 3]] > 1 &]][[All, -1, 1]] (* Michael De Vlieger, May 10 2016, after Harvey P. Dale at A001235 *)
For k = 1729 the sum of the digits is 19 and M = 1: 19 * 91 = 1729. For k = 122512 the sum of the digits is 13 and M = 31: 13 * 31 = 403 and 403 * 304 = 122512.
select( is(n,s=sumdigits(n))=n&&!frac(n/=s)&&fordiv(n,M,fromdigits(Vecrev(digits(s*M)))*M==n&&return(1)), [0..10^5]) \\ M. F. Hasler, May 27 2018
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