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.

Showing 1-4 of 4 results.

A027430 Number of distinct products i*j*k with 1 <= i < j < k <= n.

Original entry on oeis.org

0, 0, 1, 4, 10, 16, 29, 42, 60, 75, 111, 126, 177, 206, 238, 274, 361, 396, 507, 554, 613, 677, 838, 883, 1004, 1092, 1198, 1277, 1529, 1590, 1881, 1998, 2133, 2275, 2432, 2518, 2921, 3096, 3278, 3391, 3884, 4014, 4563, 4750, 4938, 5186, 5840, 5987, 6422, 6652
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

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

Links

Crossrefs

Cf. A000292, A027425, A088434, A100435, A100436.
Number of terms in row n of A083507.
Cf. A027429, A027428.

Programs

  • Haskell
    import Data.List (nub)
a027430 n = length $ nub [i*j*k | k<-[3..n], j<-[2..k-1], i<-[1..j-1]]
-- Reinhard Zumkeller, Jan 01 2012
  • Mathematica
    nn = 50;
prod = Table[0, {1 + nn^3}];
a[1] = 0;
a[n_] := (Do[prod[[1 + i*j*k]] = 1, {i, 0, n}, {j, i+1, n}, {k, j+1, n}]; Count[Take[prod, 1 + n^3], 1] - 1);
Array[a, nn] (* Jean-François Alcover, Jul 31 2018, after T. D. Noe *)
  • PARI
    \\ See PARI link. David A. Corneth, Jul 31 2018
  • Python
    def A027430(n): return len({i*j*k for i in range(1,n+1) for j in range(1,i) for k in range(1,j)}) # Chai Wah Wu, Oct 16 2023

Formula

a(n) = A027429(n)-1. - T. D. Noe, Jan 16 2007
a(n) <= A000292(n - 2). - David A. Corneth, Jul 31 2018

Extensions

Corrected by David Wasserman, Nov 18 2004

A100435 Number of distinct products i*j*k for 1 <= i <= j < k <= n.

Original entry on oeis.org

0, 1, 4, 9, 18, 26, 44, 57, 76, 93, 135, 153, 212, 245, 282, 317, 414, 452, 575, 624, 690, 759, 935, 986, 1103, 1196, 1297, 1378, 1645, 1716, 2024, 2136, 2279, 2427, 2597, 2687, 3110, 3292, 3483, 3606, 4123, 4262, 4837, 5026, 5227, 5485, 6168, 6318, 6725
Offset: 1

Views

Author

N. J. A. Sloane, Nov 21 2004

Keywords

Crossrefs

Cf. A027428, A027425, A027430, A100436.

Programs

  • Maple
    f:=proc(n) local i,j,k,t1; t1:={}; for i from 1 to n-1 do for j from i to n-1 do for k from j+1 to n do t1:={op(t1),i*j*k}; od: od: od: t1:=convert(t1,list); nops(t1); end;
  • Mathematica
    f[n_] := Length[ Union[ Flatten[ Table[ i*j*k, {i, n}, {j, i, n}, {k, j + 1, n}] ]]]; Table[ f[n], {n, 49}] (* Robert G. Wilson v, Dec 14 2004 *)
  • Python
    def A100435(n): return len({i*j*k for i in range(1,n+1) for j in range(1,i) for k in range(1,j+1)}) # Chai Wah Wu, Oct 16 2023

Extensions

More terms from Robert G. Wilson v, Dec 14 2004

A100437 Number of distinct products i*j*k*l for 1 <= i <= j <= k <= l <= n.

Original entry on oeis.org

1, 5, 15, 25, 55, 75, 140, 175, 225, 275, 448, 504, 770, 882, 1022, 1134, 1626, 1782, 2460, 2670, 2970, 3270, 4345, 4565, 5135, 5585, 6100, 6505, 8338, 8679, 10927, 11525, 12393, 13261, 14345, 14787, 18187, 19344, 20618, 21346, 25823, 26698
Offset: 1

Views

Author

N. J. A. Sloane, Nov 21 2004

Keywords

Links

Crossrefs

Cf. A027425, A027430, A100435, A100436, A100438.

Programs

  • Maple
    f:=proc(n) local i,j,k,l,t1; t1:={}; for i from 1 to n do for j from i to n do for k from j to n do for l from k to n do t1:={op(t1),i*j*k*l}; od: od: od: od: t1:=convert(t1,list); nops(t1); end;
  • Mathematica
    f[n_] := Length[ Union[ Flatten[ Table[ i*j*k*l, {i, n}, {j, i, n}, {k, j, n}, {l, k, n}] ]]]; Table[ f[n], {n, 45}] (* Robert G. Wilson v, Dec 14 2004 *)
  • PARI
    pr(n)=my(v=List());for(i=1,n, for(j=i,n, listput(v, i*j))); Set(v)
a(n)=my(u=List(),v=pr(n)); for(i=1,#v,for(j=i,#v,listput(u,v[i]*v[j]))); #Set(u) \\ Charles R Greathouse IV, Mar 04 2014

Extensions

More terms from Robert G. Wilson v, Dec 14 2004

A100438 Number of distinct products i*j*k*l for 1 <= i < j < k < l <= n.

Original entry on oeis.org

0, 0, 0, 1, 5, 13, 29, 50, 79, 111, 186, 219, 345, 428, 513, 610, 884, 991, 1387, 1535, 1742, 1994, 2671, 2833, 3319, 3719, 4154, 4474, 5751, 5985, 7575, 8121, 8803, 9593, 10401, 10785, 13303, 14371, 15414, 15988, 19379, 20089, 24103, 25237, 26369
Offset: 1

Views

Author

N. J. A. Sloane, Nov 21 2004

Keywords

Crossrefs

Cf. A027425, A027430, A100435, A100436, A100437.

Programs

  • Maple
    f:=proc(n) local i,j,k,l,t1; t1:={}; for i from 1 to n-3 do for j from i+1 to n-2 do for k from j+1 to n-1 do for l from k+1 to n do t1:={op(t1),i*j*k*l}; od: od: od: od: t1:=convert(t1,list); nops(t1); end;
  • Mathematica
    f[n_] := Length[ Union[ Flatten[ Table[ i*j*k*l, {i, n}, {j, i + 1, n}, {k, j + 1, n}, {l, k + 1, n}]]]]; Table[ f[n], {n, 45}] (* Robert G. Wilson v, Dec 14 2004 *)
  • Python
    def A100438(n): return len({i*j*k*l for i in range(1,n+1) for j in range(1,i) for k in range(1,j) for l in range(1,k)}) # Chai Wah Wu, Oct 16 2023

Extensions

More terms from Robert G. Wilson v, Dec 14 2004
Showing 1-4 of 4 results.

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

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