A022550 -id:A022550 - cp's OEIS frontend

A022549 Sum of a square and a nonnegative cube.

0, 1, 2, 4, 5, 8, 9, 10, 12, 16, 17, 24, 25, 26, 27, 28, 31, 33, 36, 37, 43, 44, 49, 50, 52, 57, 63, 64, 65, 68, 72, 73, 76, 80, 81, 82, 89, 91, 100, 101, 108, 113, 121, 122, 125, 126, 127, 128, 129, 134, 141, 144, 145

Offset: 1

N. J. A. Sloane

It appears that there are no modular constraints on this sequence; i.e., every residue class of every integer has representatives here. - Franklin T. Adams-Watters, Dec 03 2009

A045634(a(n)) > 0. - Reinhard Zumkeller, Jul 17 2010

R. Zumkeller, Table of n, a(n) for n = 1..10000 - _Reinhard Zumkeller_, Jul 17 2010

Complement of A022550; A002760 and A179509 are subsequences.

Cf. A055394, A045634, A055393, A123291, A169618, A123364, A111925.

q=30; imax=q^2; Select[Union[Flatten[Table[x^2+y^3, {y,0,q^(2/3)}, {x,0,q}]]], #<=imax&] (* Vladimir Joseph Stephan Orlovsky, Apr 20 2011 *)

is(n)=for(k=0,sqrtnint(n,3), if(issquare(n-k^3), return(1))); 0 \\ Charles R Greathouse IV, Aug 24 2020

list(lim)=my(v=List(),t); for(k=0,sqrtnint(lim\=1,3), t=k^3; for(n=0,sqrtint(lim-t), listput(v,t+n^2))); Set(v) \\ Charles R Greathouse IV, Aug 24 2020

A045634 Number of ways in which n can be partitioned as a sum of a square and cube.

Original entry on oeis.org

1, 2, 1, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2

Offset: 0

Felice Russo

nonn

a(A022550(n))=0; a(A179509(n))=1; a(A022549(n))>0; a(A060861(n))=n. [From Reinhard Zumkeller, Jul 17 2010]

			a(9)=2 because 9=2^3+1^2 and 9=3^2+0^3.

T. D. Noe, Table of n, a(n) for n = 0..10000

Cf. A022549, A060861, A135910, A135911, A135912.

M:=100; M2:=M^2; t0:=array(0..M2);
for i from 0 to M2 do t0[i]:=0; od:
for a from 0 to M do for b from 0 to M do
i:=a^2+b^3; if i <= M2 then t0[i]:=t0[i]+1; fi; od: od:
[seq(t0[i],i=0..M2)];

max = 100; Clear[a]; a[_] = 0;
Do[n = i^2 + j^3; a[n] += 1, {i, 0, Sqrt[max]}, {j, 0, max^(1/3)}];
Table[a[n], {n, 0, max}] (* Jean-François Alcover, Aug 02 2018 *)

More terms from Erich Friedman

A123291 Numbers that are sum of a square and a nonnegative cube (with repetition).

Original entry on oeis.org

0, 1, 1, 2, 4, 5, 8, 9, 9, 10, 12, 16, 17, 17, 24, 25, 26, 27, 28, 31, 33, 36, 36, 37, 43, 44, 49, 50, 52, 57, 63, 64, 64, 65, 65, 68, 72, 73, 76, 80, 81, 82, 89, 89, 91, 100, 100, 101, 108, 108, 113, 121, 122, 125, 126, 127, 128, 129, 129, 134, 141, 144, 145, 145, 148

Offset: 1

Zak Seidov, Oct 11 2006

nonn

Cf. A022549 Sum of a square and a nonnegative cube (without repetition), A022550 Numbers that are not the sum of a square and a nonnegative cube.

			Each of 1, 9, 17, 36 appear two times because
1=0^2+1^3=1^2+0^3, 9=1^2+2^3=3^2+0^3, 17=3^2+2^3==4^2+1^3, 36=3^2+3^3==6^2+0^3;
225 appears three times because 225=3^2+6^3=10^2+5^3=15^2+0^3;
1025 appears four times because 1025=5^2+10^3=30^2+5^3=31^2+4^3=32^2+1^3, etc.

Cf. A022549, A022550.

Lim=148; s=Ceiling[Sqrt[Lim]];c=Ceiling[Lim^(1/3)];sq=Range[0,s]^2;cb=Range[0,c]^3;seq={};Do[AppendTo[seq,sq[[i]]+cb[[j]]],{i,s+1},{j,c+1}];Sort[Select[seq,#<=Lim&]] (* James C. McMahon, Nov 19 2024 *)

A214922 Numbers of the form x^2 + y^2 + z^3 + w^3 (x, y, z, w >= 0).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54

Offset: 1

Philippe Deléham, Jul 20 2012

nonn

Conjecture: 23 is the only number not in this sequence.
Not the same as A004830: 239 is a term of this sequence but not of A004830. - R. J. Mathar and Joerg Arndt, Jul 28 2012
There are no other missing numbers from 24 to 10^8. - Giovanni Resta, Oct 12 2019

			22 = 2^2 + 4^2 + 1^3 + 1^3, 22 is in this sequence.

Cf. A001481, A004999, A022549, A022550, A022551, A022552.

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A022549 Sum of a square and a nonnegative cube.

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A045634 Number of ways in which n can be partitioned as a sum of a square and cube.

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A123291 Numbers that are sum of a square and a nonnegative cube (with repetition).

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A214922 Numbers of the form x^2 + y^2 + z^3 + w^3 (x, y, z, w >= 0).

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