cp's OEIS Frontend

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.

Previous Showing 11-16 of 16 results.

A226600 Number of ordered triples (i,j,k) with i*j*k <= n and i,j,k >= 0.

Original entry on oeis.org

1, 8, 23, 44, 74, 107, 152, 197, 255, 315, 384, 453, 543, 624, 717, 816, 927, 1032, 1158, 1275, 1413, 1548, 1689, 1830, 2004, 2160, 2325, 2497, 2683, 2860, 3067, 3256, 3469, 3676, 3889, 4108, 4360, 4585, 4822, 5065, 5335, 5584, 5863, 6124, 6406, 6694, 6979
Offset: 0

Views

Author

Robert Price, Jun 13 2013

Keywords

Links

Crossrefs

Cf. A100450, A226357, A226359.

Programs

  • Mathematica
    f[n_] := Length[Complement[Union[Flatten[Table[If[i*j*k <= n, {i, j, k}], {i, 0, n}, {j, 0, n}, {k, 0, n}], 2]], {Null}]]; Table[f[n], {n, 0, 100}]

Formula

a(n) = A003215(n) + A061201(n). - Alois P. Heinz, Jun 13 2013

A225523 Number of distinct products i*j over all pairs (i,j) with |i| + |j| <= n.

Original entry on oeis.org

1, 1, 3, 5, 9, 11, 17, 21, 27, 33, 39, 43, 53, 59, 69, 79, 89, 97, 107, 117, 131, 143, 157, 167, 183, 195, 209, 223, 237, 249, 269, 283, 301, 317, 335, 353, 373, 389, 409, 427, 449, 465, 491, 509, 535, 557, 581, 603, 631, 657, 679
Offset: 0

Views

Author

Robert Price, May 09 2013

Keywords

Comments

This sequence is in reply to an extension request made in A100449.

Links

Crossrefs

Cf. A018805, A027430, A100448, A100449, A100450, A213207.

Programs

  • Mathematica
    f[n_]:=Length[Complement[Union[Flatten[Table[If[Abs[i]+Abs[j]<=n,{i*j}],{i,-n,n},{j,-n,n}],1]],{Null}]]; Table[f[n],{n,0,100}]

A225526 Number of distinct products i*j over all pairs (i,j) with |i| + |j| <= n and gcd(i,j) <= 1.

Original entry on oeis.org

1, 1, 3, 5, 7, 11, 13, 17, 21, 27, 31, 39, 43, 51, 57, 63, 69, 81, 87, 99, 107, 117, 125, 139, 147, 159, 169, 183, 195, 215, 223, 241, 257, 273, 287, 305, 315, 339, 353, 371, 383, 407, 419, 443, 461, 479, 497, 523, 539, 567, 585
Offset: 0

Views

Author

Robert Price, May 09 2013

Keywords

Comments

This sequence is in reply to an extension request made in A100449.
Note that gcd(0,m) = m for any m.

Links

Crossrefs

Cf. A018805, A027430, A100448, A100449, A100450, A213208.

Programs

  • Mathematica
    f[n_]:=Length[Complement[Union[Flatten[Table[If[Abs[i]+Abs[j]<=n&&GCD[i,j]<=1, {i*j}], {i, -n, n}, {j, -n, n}], 1]], {Null}]]; Table[f[n], {n, 0, 100}]

A225527 Number of distinct products i*j over all pairs (i,j) with i,j>=0 and i+j <= n.

Original entry on oeis.org

1, 1, 2, 3, 5, 6, 9, 11, 14, 17, 20, 22, 27, 30, 35, 40, 45, 49, 54, 59, 66, 72, 79, 84, 92, 98, 105, 112, 119, 125, 135, 142, 151, 159, 168, 177, 187, 195, 205, 214, 225, 233, 246, 255, 268, 279, 291, 302, 316, 329, 340, 352, 367, 377, 392
Offset: 0

Views

Author

Robert Price, May 09 2013

Keywords

Comments

This sequence is in reply to an extension request made in A100449.

Links

Crossrefs

Cf. A018805, A027430, A100448, A100449, A100450, A213207, A213208.

Programs

  • Mathematica
    f[n_]:=Length[Complement[Union[Flatten[Table[If[i+j≤n,{i*j}],{i,0,n},{j,0,n}],1]],{Null}]]; Table[f[n],{n,0,100}]

A225529 Number of distinct products i*j over all pairs (i,j) with i,j >= 0 and i+j <= n and gcd(i,j) <= 1.

Original entry on oeis.org

1, 1, 2, 3, 4, 6, 7, 9, 11, 14, 16, 20, 22, 26, 29, 32, 35, 41, 44, 50, 54, 59, 63, 70, 74, 80, 85, 92, 98, 108, 112, 121, 129, 137, 144, 153, 158, 170, 177, 186, 192, 204, 210, 222, 231, 240, 249, 262, 270, 284, 293, 305, 315, 331, 340, 353
Offset: 0

Views

Author

Robert Price, May 09 2013

Keywords

Comments

Note that gcd(0,m) = m for any m.

Links

Crossrefs

Cf. A018805, A027430, A100448, A100449, A100450, A213207, A213208.

Programs

  • Mathematica
    f[n_]:=Length[Complement[Union[Flatten[Table[If[i+j≤n&&GCD[i,j]<=1, {i*j}], {i, 0, n}, {j, 0, n}], 1]], {Null}]]; Table[f[n], {n, 0, 100}]

A226601 Number of ordered triples (i,j,k) with i*j*k <= n, i,j,k >= 0 and gcd{i,j,k} <= 1.

Original entry on oeis.org

1, 8, 17, 32, 50, 77, 98, 137, 170, 212, 245, 308, 350, 425, 470, 527, 587, 686, 740, 851, 917, 998, 1067, 1202, 1277, 1403, 1484, 1601, 1691, 1862, 1937, 2120, 2231, 2360, 2465, 2618, 2726, 2945, 3062, 3215, 3338, 3581, 3680, 3935, 4073, 4235, 4376, 4655
Offset: 0

Views

Author

Robert Price, Jun 13 2013

Keywords

Comments

Note that gcd(0,m) = m for any m.

Links

Crossrefs

Cf. A100450, A226357, A226359, A226600.

Programs

  • Mathematica
    f[n_] := Length[Complement[Union[Flatten[Table[If[i*j*k <= n && GCD[i, j, k] ≤ 1, {i, j, k}], {i, 0, n}, {j, 0, n}, {k, 0, n}], 2]], {Null}]]; Table[f[n], {n, 0, 100}]
Previous Showing 11-16 of 16 results.

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