A122723 -id:A122723 - cp's OEIS frontend

A024975 Sums of three distinct positive cubes.

36, 73, 92, 99, 134, 153, 160, 190, 197, 216, 225, 244, 251, 281, 288, 307, 342, 349, 352, 368, 371, 378, 405, 408, 415, 434, 469, 476, 495, 521, 532, 540, 547, 560, 567, 577, 584, 586, 603, 623, 638, 645, 664, 684, 701, 729, 736, 738, 755, 757, 764, 792, 794, 801, 820

Offset: 1

Clark Kimberling

nonn

Subsequence of A003072. Equals A024973 if duplicates of repeated entries are removed. - R. J. Mathar, Apr 13 2008

T. D. Noe, Table of n, a(n) for n = 1..10000

Cf. A122723 (primes in here), A025399-A025402, A025411 (4 distinct positive cubes).

Total/@Subsets[Range[10]^3,{3}]//Union (* Harvey P. Dale, Aug 22 2021 *)

list(lim)=my(v=List(),x3,t); lim\=1; for(x=3,sqrtnint(lim-9,3), x3=x^3; for(y=2,min(x-1,sqrtnint(lim-x3-1,3)), t=x3+y^3; for(z=1,min(y-1,sqrtnint(lim-t,3)), listput(v,t+z^3)))); Set(v) \\ Charles R Greathouse IV, Sep 20 2016

{n: A025469(n) >= 1}. - R. J. Mathar, Jun 15 2018

Verified by Don Reble, Nov 19 2006

A137365 Prime numbers n such that n = p1^3 + p2^3 + p3^3, a sum of cubes of 3 distinct prime numbers.

Original entry on oeis.org

1483, 5381, 6271, 7229, 9181, 11897, 13103, 13841, 14489, 17107, 20357, 25747, 26711, 27917, 30161, 30259, 31247, 32579, 36161, 36583, 36677, 36899, 36901, 42083, 48817, 54181, 55511, 55691, 56377, 56897, 57637, 59093, 64151, 66347

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 09 2008

nonn

Numbers n may have multiple decompositions; for example, n=185527 and n=451837 have two, and n=8627527 and n=32816503 have three. The smallest n with more than one decomposition is n = 185527 = 13^3+43^3+47^3 = 19^3+31^3+53^3, the 94th in the sequence. - R. J. Mathar, May 01 2008
Primes in A138853 and A138854. - M. F. Hasler, Apr 13 2008
The least prime, p, which has n decompositions {with its primes} is 1483 = {3, 5, 11}; 185527 = {13, 43, 47} & {19, 31, 53}; 8627527 = {19, 151, 173}, {33, 139, 181} & {71, 73, 199} and 1122871751 = {113, 751, 887}, {131, 701, 919}, {151, 659, 941} & {29, 107, 1039}. - Robert G. Wilson v, May 04 2008
The number of terms < 10^n: 0, 0, 0, 5, 56, 327, 2172, 13417, 86264, 567211, ..., . - Robert G. Wilson v, May 04 2008
The number of decompositions < 10^n: 0, 0, 0, 5, 56, 330, 2201, 13609, 87200, 571770, ..., . - Robert G. Wilson v, May 04 2008

			1483=3^3+5^3+11^3, 5381=17^3+7^3+5^3, 6271=3^3+11^3+17^3, etc.

Robert G. Wilson v, Table of n, a(n) for n = 1..13418 (duplicates omitted)
Robert G. Wilson v, Table of n, a(n) for n = 1..13610 (duplicates included)
Index to sequences related to sums of cubes.

Cf. A137366.

Cf. A024975 (a^3+b^3+c^3, a>b>c>0), A122723 (primes in A024975), A138853-A138854.

# From R. J. Mathar: (Start)
isA030078 := proc(n) local cbr; cbr := floor(root[3](n)) ; if cbr^3 = n and isprime(cbr) then true ; else false; fi ; end:
isA137365 := proc(n) local p1,p2,p3,p3cub ; if isprime(n) then p1 := 2 ; while p1^3 <= n-16 do p2 := nextprime(p1) ; while p1^3+p2^3 <= n-8 do p3cub := n-p1^3-p2^3 ; if p3cub> p2^3 and isA030078(p3cub) then RETURN(true) ; fi ; p2 := nextprime(p2) ; od: p1 := nextprime(p1) ; od; RETURN(false) ; else RETURN(false) ; fi ; end:
for i from 1 do if isA137365( ithprime(i)) then printf("%d\n",ithprime(i)) ; fi ; od:
# (End)

Array[r, 99]; Array[y, 99]; For[i = 0, i < 10^2, r[i] = y[i] = 0; i++ ]; z = 4^2; n = 0; For[i1 = 1, i1 < z, a = Prime[i1]; a2 = a^3; For[i2 = i1 + 1, i2 < z, b = Prime[i2]; b2 = b^3; For[i3 = i2 + 1, i3 < z, c = Prime[i3]; c2 = c^3; p = a2 + b2 + c2; If[PrimeQ[p], Print[a2, " + ", b2, " + ", c2, " = ", p]; n++; r[n] = p]; i3++ ]; i2++ ]; i1++ ]; Sort[Array[r, 88]] (* Vladimir Joseph Stephan Orlovsky *)
lst = {}; Do[p = Prime[q]^3 + Prime[r]^3 + Prime[s]^3; If[PrimeQ@ p, AppendTo[lst, p]], {q, 13}, {r, q - 1}, {s, r - 1}]; Take[Sort@ lst, 36] (* Robert G. Wilson v, Apr 13 2008 *)
nn=20; lim=Prime[nn]^3+3^3+5^3; Union[Select[Total[#^3]& /@ Subsets[Prime[Range[2,nn]], {3}], #Harvey P. Dale, Jan 15 2011 *)

c=0; forprime(p=1,10^6, isA138853(p) & write("b137365.txt",c++," ",p)) \\ M. F. Hasler, Apr 13 2008

A137365 = A000040 intersect A138853 = A000040 intersect A138854. - M. F. Hasler, Apr 13 2008

Corrected and extended by Zak Seidov, R. J. Mathar and Robert G. Wilson v, Apr 12 2008

Further edits by R. J. Mathar and N. J. A. Sloane, Jun 07 2008

A306213 Numbers that are the sum of cubes of three distinct positive integers in arithmetic progression.

Original entry on oeis.org

36, 99, 153, 216, 288, 405, 408, 495, 645, 684, 792, 855, 972, 1071, 1197, 1224, 1407, 1548, 1584, 1701, 1728, 1968, 2079, 2241, 2304, 2403, 2541, 2673, 2736, 3051, 3060, 3240, 3264, 3537, 3540, 3888, 3960, 4059, 4131, 4257, 4500, 4587, 4833, 5049, 5160, 5256, 5472, 5643, 5832, 5940, 6336, 6369, 6669

Offset: 1

Antonio Roldán, Jan 29 2019

nonn

Numbers that can be written as 3*a*(a^2 + 2*b^2) = (a-b)^3 + a^3 + (a+b)^3 where 0 < b < a. - Robert Israel, Dec 15 2022

			153 = 1^3 + 3^3 + 5^3, with 3 - 1 = 5 - 3 = 2;
972 = 3^3 + 6^3 + 9^3, with 6 - 3 = 9 - 6 = 3.

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

Cf. A000578, A023042, A024975, A122723, A306212, A306214.

N:= 10000: # for terms <= N
S:= {}:
for a from 1 while a^3 + (a+1)^3 + (a+2)^3 <= N do
  for d from 1 do
    x:= a^3 + (a+d)^3 + (a+2*d)^3;
    if x > N then break fi;
    S:= S union {x}
od od:
sort(convert(S,list)); # Robert Israel, Dec 14 2022

for(n=3, 7000, k=(n/3)^(1/3); a=2; v=0; while(a<=k&&v==0, b=(n-3*a^3)/(6*a); if(b==truncate(b)&&issquare(b), d=sqrt(b), d=0); if(d>=1&&d<=a-1, v=1; print1(n,", ")); a+=1))

w=List(); for(n=3, 7000, k=(n/3)^(1/3); for(a=2, k, for(c=1, a-1, v=(a-c)^3+a^3+(a+c)^3; if(v==n, listput(w,n))))); print(vecsort(Vec(w),,8))

A180088 Primes which are the sum of three distinct positive cubes in two or more distinct ways.

Original entry on oeis.org

1009, 4229, 4447, 4733, 6301, 7561, 10657, 12377, 12979, 13103, 13859, 14561, 15569, 15667, 17207, 20663, 20747, 20899, 21673, 22511, 24137, 24499, 25999, 27793, 27917, 28001, 28493, 28729, 29917, 31123, 32579, 32833, 32957, 33119

Offset: 1

Vladimir Joseph Stephan Orlovsky, Aug 09 2010

nonn

1^3+2^3+10^3=1009=4^3+6^3+9^3

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A011541, A024974, A025400, A122723

lst1=Sort@Select[Flatten[Table[a^3+b^3+c^3,{a,1,66},{b,a-1,1,-1},{c,b-1,1,-1}]],PrimeQ[ # ]&]; lst={};Do[If[lst1[[n]]==lst1[[n+1]],AppendTo[lst,lst1[[n]]]],{n,Length[lst1]-1}];lst

A180089 Semiprimes which are the sum of three distinct positive cubes in two or more distinct ways.

Original entry on oeis.org

1366, 1457, 1793, 1945, 3599, 4105, 5435, 7379, 8315, 9017, 10261, 10963, 11773, 12706, 13957, 15163, 15371, 15553, 15751, 15758, 16271, 17263, 17354, 17947, 18649, 19027, 19369, 19657, 19729, 19774, 19781, 19907, 21026, 21167, 22411

Offset: 1

Vladimir Joseph Stephan Orlovsky, Aug 09 2010

nonn

2^3+3^3+11^3=5^3+8^3+9^3=1366=2*683, 1^3+5^3+11^3=6^3+8^3+9^3=1457=31*47,..

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A011541, A024974, A025400, A122723, A180088

f[n_]:=Last/@FactorInteger[n]=={1,1}; lst={};Do[Do[Do[If[f[p=a^3+b^3+c^3],AppendTo[lst,p]],{c,b-1,1,-1}],{b,a-1,1,-1}],{a,55}];lst1=Sort@lst; lst={};Do[If[lst1[[n]]==lst1[[n+1]],AppendTo[lst,lst1[[n]]]],{n,Length[lst1]-1}];lst

A180099 Primes which are the sum of three distinct positive cubes of prime numbers in two or more distinct ways.

Original entry on oeis.org

185527, 451837, 591751, 1265471, 1266929, 1618973, 1626227, 1664713, 2586277, 2754683, 2765519, 2805193, 3422303, 3740309, 3748499, 4154779, 5336479, 5483953, 5557987, 6130151, 6586091, 7231013, 7361801, 7726571, 8205553

Offset: 1

Vladimir Joseph Stephan Orlovsky, Aug 09 2010

nonn

			185527 = 47^3+43^3+13^3=53^3+31^3+19^3.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A011541, A024974, A025400, A122723, A180088, A180089.

lst={};Do[Do[Do[If[PrimeQ[p=Prime[a]^3+Prime[b]^3+Prime[c]^3],AppendTo[lst,p]],{c,b-1,1,-1}],{b,a-1,1,-1}],{a,88}];lst1=Sort@lst; lst={};Do[If[lst1[[n]]==lst1[[n+1]],AppendTo[lst,lst1[[n]]]],{n,Length[lst1]-1}];lst
Select[Tally[Select[Total/@Subsets[Prime[Range[50]]^3,{3}],PrimeQ]],#[[2]]> 1&] [[All,1]]//Sort (* Harvey P. Dale, Sep 26 2020 *)

A385094 Primes that are the sum of distinct positive cubes.

Original entry on oeis.org

73, 197, 251, 281, 307, 349, 379, 433, 443, 503, 521, 541, 547, 577, 587, 631, 659, 673, 701, 709, 719, 757, 821, 827, 829, 853, 863, 881, 883, 919, 947, 953, 1009, 1091, 1097, 1153, 1163, 1171, 1217, 1223, 1231, 1249, 1277, 1289, 1297, 1307, 1361, 1367, 1423, 1433, 1439, 1483, 1493

Offset: 1

Zhining Yang, Jun 17 2025

12101 is the largest of 421 primes not in this sequence.

			757 is in the sequence because prime 757 = 1^3 + 3^3 + 9^3 = 1^3 + 2^3 + 4^3 + 5^3 + 6^3 + 7^3.

Zhining Yang, Table of n, a(n) for n = 1..1030

Cf. A003997, A122723.

m = 15; a = {0}; Do[a = Select[Union[a, a + k^3], # < m^3 &], {k, m}];
a = Select[PrimeQ]@a

For n > 1027, a(n) = prime(n + 421).

A180106 Semiprimes which are the sum of three distinct positive cubes of semiprime numbers in two or more distinct ways.

Original entry on oeis.org

88073, 195905, 196057, 196841, 205102, 211466, 610903, 747209, 809966, 1078622, 1543267, 1828441, 1967402, 2143783, 2312029, 2803501, 3055258, 3108673, 3244466, 3477629, 3662567, 4237577, 4770137, 5741074, 5835593, 5908889, 7189265, 7497118, 8438249, 8742781

Offset: 1

Vladimir Joseph Stephan Orlovsky, Aug 10 2010

nonn

610903 = 74^3+55^3+34^3 = 82^3+39^3+6^3.

88073 = 29*3037 = 21^3+33^3+35^3 = 25^3+26^3+38^3. - Chai Wah Wu, May 20 2017

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A011541, A024974, A025400, A122723, A180088, A180089, A180099

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 *)

Terms corrected by Chai Wah Wu, May 20 2017

cp's OEIS Frontend

A024975 Sums of three distinct positive cubes.

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A137365 Prime numbers n such that n = p1^3 + p2^3 + p3^3, a sum of cubes of 3 distinct prime numbers.

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A306213 Numbers that are the sum of cubes of three distinct positive integers in arithmetic progression.

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A180088 Primes which are the sum of three distinct positive cubes in two or more distinct ways.

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A180089 Semiprimes which are the sum of three distinct positive cubes in two or more distinct ways.

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A180099 Primes which are the sum of three distinct positive cubes of prime numbers in two or more distinct ways.

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A385094 Primes that are the sum of distinct positive cubes.

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A180106 Semiprimes which are the sum of three distinct positive cubes of semiprime numbers in two or more distinct ways.

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