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 21-26 of 26 results.

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}]

A083507 n-th row of the following triangle contains all distinct numbers that can be obtained as the product of three distinct numbers chosen from 1 to n (for n>2). Sequence contains the triangle read by rows.

Original entry on oeis.org

6, 6, 8, 12, 24, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 6, 8, 10, 12, 15, 18, 20, 24, 30, 36, 40, 48, 60, 72, 90, 120, 6, 8, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 48, 56, 60, 70, 72, 84, 90, 105, 120, 126, 140, 168, 210, 6, 8, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28
Offset: 3

Views

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 05 2003

Keywords

Examples

			6
6,8,12,24
6,8,10,12,15,20,24,30,40,60
6,8,10,12,15,18,20,24,30,36,40,48,60,72,90
...

References

  • Amarnath Murthy, Generalization of partition function introducing Smarandache Factor Partitions, Smarandache Notions Journal, 1-2-3, Vol. 11, 2000.

Crossrefs

Numbers of terms in rows are given by A027430.

Extensions

More terms from David Wasserman, Nov 18 2004

A083508 Number of distinct products i*j*k with 1 <= i < j <= k <= n and j < n.

Original entry on oeis.org

0, 0, 2, 7, 16, 24, 40, 56, 77, 96, 137, 158, 214, 249, 284, 322, 418, 464, 583, 645, 708, 774, 946, 1007, 1125, 1220, 1330, 1420, 1685, 1768, 2069, 2203, 2346, 2492, 2658, 2750, 3166, 3362, 3553, 3675, 4183, 4344, 4909, 5129, 5327, 5575, 6252, 6432, 6849
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A027430, A100435.

Programs

  • Maple
    V:= Vector(100):
S:= {}:
for n from 1 to 100 do
  S:= S union {seq(i*(n-1)^2, i=1..n-2), seq(seq(i*j*n, i=1..j-1),j=2..n-1)};
  V[n]:= nops(S);
od:
convert(V,list); # Robert Israel, Aug 03 2025
  • PARI
    for(n=1,100,s=Set();for(i=1,n-2,for(j=i+1,n-1,for(k=j,n,p=i*j*k;if(!setsearch(s,p),s=setunion(s,Set(p))))));print1(length(s),",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 06 2006

Extensions

Better definition and more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 06 2006
Definition corrected by Robert Israel, Aug 03 2025
Previous Showing 21-26 of 26 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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