A344804 -id:A344804 - cp's OEIS frontend

A025397 Numbers that are the sum of 3 positive cubes in exactly 3 ways.

5104, 9729, 12104, 12221, 12384, 14175, 17604, 17928, 19034, 20691, 21412, 21888, 24480, 28792, 29457, 30528, 31221, 32850, 34497, 35216, 36288, 38259, 39339, 39376, 40060, 40097, 40832, 40851, 41033, 41040, 41364, 41966, 42056, 42687, 43408, 45144

Offset: 1

David W. Wilson

nonn

Donovan Johnson, Table of n, a(n) for n = 1..10000

Cf. A008917, A025323, A025396, A025398, A025405, A025456, A343969, A344240, A344804.

N:= 10^5: # to get all terms <= N
Reps:= Matrix(N,3,(i,j) -> {}):
for i from 1 to floor(N^(1/3)) do
  Reps[i^3,1]:= {[i]}
od:
for j from 2 to 3 do
for i from 1 to floor(N^(1/3)) do
  for x from i^3+1 to N do
    Reps[x,j]:= Reps[x,j] union
      map(t -> if t[-1] <= i then [op(t),i] fi, Reps[x-i^3,j-1]);
  od
od
od:
select(t -> nops(Reps[t,3])=3, [$1..N]); # Robert Israel, Aug 28 2015

Reap[ For[ n = 1, n <= 50000, n++, pr = Select[ PowersRepresentations[n, 3, 3], Times @@ # != 0 &]; If[pr != {} && Length[pr] == 3, Print[n, pr]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Jul 31 2013 *)

is(n)=k=ceil((n-2)^(1/3)); d=0; for(a=1, k, for(b=a, k, for(c=b, k, if(a^3+b^3+c^3==n, d++)))); d
n=3; while(n<50000, if(is(n)==3, print1(n, ", ")); n++) \\ Derek Orr, Aug 27 2015

n such that A025456(n) = 3. - Robert Israel, Aug 28 2015

A018787 Numbers that are the sum of two positive cubes in at least three ways (all solutions).

Original entry on oeis.org

87539319, 119824488, 143604279, 175959000, 327763000, 700314552, 804360375, 958595904, 1148834232, 1407672000, 1840667192, 1915865217, 2363561613, 2622104000, 3080802816, 3235261176, 3499524728, 3623721192, 3877315533, 4750893000, 5544709352, 5602516416

Offset: 1

David W. Wilson, Aug 15 1996

nonn

J. Leech, Some solutions of Diophantine equations, Proc. Camb. Phil. Soc., 53 (1957), 778-780.
R. K. Guy, Unsolved Problems in Number Theory, D1.

Ray Chandler, Table of n, a(n) for n=1..100000
Uwe Hollerbach, Taxi, Taxi! [Original link, broken]
Uwe Hollerbach, Taxi, Taxi! [Replacement link to Wayback Machine]
Uwe Hollerbach, Taxi! Taxi! [Cached copy from Wayback Machine, html version of top page only]

Cf. A001235, A003825, A023051, A025294, A025398, A344804.

a=Sort[Flatten@Table[n^3+m^3,{m,2000},{n,m-1,1,-1}]];f3[l_]:=Module[{t={}},Do[If[l[[n]]==l[[n+2]],AppendTo[t,l[[n]]]],{n,1,Length[l]-2}];t];f3[a] (* Vladimir Joseph Stephan Orlovsky, Jan 21 2012 *)

A343708 Numbers that are the sum of two positive cubes in exactly two ways.

Original entry on oeis.org

1729, 4104, 13832, 20683, 32832, 39312, 40033, 46683, 64232, 65728, 110656, 110808, 134379, 149389, 165464, 171288, 195841, 216027, 216125, 262656, 314496, 320264, 327763, 373464, 402597, 439101, 443889, 513000, 513856, 515375, 525824, 558441, 593047, 684019, 704977, 805688, 842751, 885248, 886464

Offset: 1

David Consiglio, Jr., Apr 26 2021

This sequence differs from A001235 at term 455 because 87539319 = 167^3 + 436^3 = 228^3 + 423^3 = 255^3 + 414^3 = A011541(3). Thus, this term is not in this sequence but is in A001235.

			13832 is in this sequence because 13832 = 2^3 + 24^3 = 18^3 + 20^3.

David Consiglio, Jr., Table of n, a(n) for n = 1..1000

Cf. A001235, A025285, A025396, A338667, A344804.

Select[Range@70000,Length@Select[PowersRepresentations[#,2,3],FreeQ[#,0]&]==2&] (* Giorgos Kalogeropoulos, Apr 26 2021 *)

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1,1000)]#n
for pos in cwr(power_terms,2):#m
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v == 2])#s
for x in range(len(rets)):
    print(rets[x])

A345865 Numbers that are the sum of two cubes in exactly four ways.

Original entry on oeis.org

6963472309248, 12625136269928, 21131226514944, 26059452841000, 55707778473984, 74213505639000, 95773976104625, 101001090159424, 159380205560856, 169049812119552, 174396242861568, 188013752349696, 208475622728000, 300656502205416, 340878679288056

Offset: 1

David Consiglio, Jr., Jul 05 2021

nonn

Differs from A023051 at term 143 because 48988659276962496 = 331954^3 + 231518^3 = 336588^3 + 221424^3 = 342952^3 + 205292^3 = 362753^3 + 107839^3 = 365757^3 + 38787^3.

			12625136269928 is a term because 12625136269928 = 21869^3 + 12939^3 = 22580^3 + 10362^3 = 23066^3 + 7068^3 = 23237^3 + 4275^3.

Sean A. Irvine, Table of n, a(n) for n = 1..154

Cf. A023051, A025287, A343969, A344804.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1, 1000)]
for pos in cwr(power_terms, 2):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 4])
    for x in range(len(rets)):
        print(rets[x])

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A025397 Numbers that are the sum of 3 positive cubes in exactly 3 ways.

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A018787 Numbers that are the sum of two positive cubes in at least three ways (all solutions).

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A343708 Numbers that are the sum of two positive cubes in exactly two ways.

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A345865 Numbers that are the sum of two cubes in exactly four ways.

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