A061791 -id:A061791 - cp's OEIS frontend

A374707 Number of distinct sums i^3 + j^3 for 0<=i<=j<=n.

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 90, 104, 119, 135, 151, 169, 188, 208, 229, 251, 274, 298, 322, 348, 375, 402, 431, 461, 492, 524, 556, 590, 623, 659, 695, 733, 772, 811, 851, 893, 936, 980, 1025, 1071, 1118, 1166, 1213, 1263, 1314, 1365, 1418, 1471, 1525, 1580, 1637, 1695, 1753

Offset: 0

Seiichi Manyama, Jul 17 2024

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Cf. A374710, A374711.

Cf. A047800, A061791.

a(n) = my(v=vector(2*n^3+1)); for(i=0, n, for(j=i, n, v[i^3+j^3+1]+=1)); sum(i=1, #v, v[i]>0);

A374714 Number of distinct sums i^3 + j^3 + k^3 + l^3 for 1<=i<=j<=k<=l<=n.

Original entry on oeis.org

1, 5, 15, 35, 70, 119, 202, 317, 473, 671, 902, 1138, 1515, 2008, 2521, 3039, 3758, 4592, 5539, 6657, 7879, 9209, 10797, 12304, 14243, 16371, 18348, 21006, 23816, 26563, 29848, 33046, 36698, 40190, 44885, 49068, 54040, 59479, 64762, 70420, 76810, 83414, 90659, 98158, 105838, 114127, 123048

Offset: 1

Seiichi Manyama, Jul 17 2024

nonn

Cf. A061791, A374713.

Cf. A374711, A374716.

a(n) = my(v=vector(4*n^3)); for(i=1, n, for(j=i, n, for(k=j, n, for(l=k, n, v[i^3+j^3+k^3+l^3]+=1)))); sum(i=1, #v, v[i]>0);

def A374714(n): return len({i**3+j**3+k**3+l**3 for i in range(1,n+1) for j in range(i,n+1) for k in range(j,n+1) for l in range(k,n+1)}) # Chai Wah Wu, Jul 18 2024

A061798 Number of sums i^3 + j^3 that occur more than once for 1<=i<=j<=n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 7, 7, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 13, 13, 14, 15, 16, 16, 16, 17, 17, 19, 19, 19, 19, 20, 20, 20, 21, 23, 24, 24, 24, 25, 25, 25, 25

Offset: 1

Labos Elemer, Jun 22 2001

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Cf. A000217, A011541, A061791.

a(n) = my(v=vector(2*n^3, i, 0)); for(i=1, n, for(j=i, n, v[i^3+j^3]+=1)); sum(i=1, #v, v[i]>1); \\ Seiichi Manyama, May 14 2024

def A(n)
  h = {}
  (1..n).each{|i|
    (i..n).each{|j|
      k = i * i * i + j * j * j
      if h.has_key?(k)
        h[k] += 1
      else
        h[k] = 1
      end
    }
  }
  h.to_a.select{|i| i[1] > 1}.size
end
def A061798(n)
  (1..n).map{|i| A(i)}
end
p A061798(80) # Seiichi Manyama, May 14 2024

A374713 Number of distinct sums i^3 + j^3 + k^3 for 1<=i<=j<=k<=n.

Original entry on oeis.org

1, 4, 10, 20, 35, 55, 83, 119, 164, 218, 280, 343, 431, 535, 648, 760, 903, 1064, 1241, 1442, 1659, 1891, 2151, 2409, 2714, 3044, 3369, 3754, 4160, 4582, 5044, 5499, 6015, 6500, 7094, 7669, 8308, 8990, 9683, 10394, 11180, 12010, 12876, 13773, 14720, 15693, 16721, 17705, 18845, 20010

Offset: 1

Seiichi Manyama, Jul 17 2024

nonn

Cf. A061791, A374714.

Cf. A374715.

a(n) = my(v=vector(3*n^3)); for(i=1, n, for(j=i, n, for(k=j, n, v[i^3+j^3+k^3]+=1))); sum(i=1, #v, v[i]>0);

cp's OEIS Frontend

A374707 Number of distinct sums i^3 + j^3 for 0<=i<=j<=n.

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A374714 Number of distinct sums i^3 + j^3 + k^3 + l^3 for 1<=i<=j<=k<=l<=n.

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A061798 Number of sums i^3 + j^3 that occur more than once for 1<=i<=j<=n.

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A374713 Number of distinct sums i^3 + j^3 + k^3 for 1<=i<=j<=k<=n.

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