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.

A064454 Erroneous version of A064461.

Original entry on oeis.org

2, 4, 13, 8, 9, 12, 17, 20
Offset: 0

Views

Author

Robert G. Wilson v, Oct 02 2001

Keywords

Examples

			a(2) = 13 because C(13,5) = 3^2*11*13 and C(13,6) = 2^2*3*11*13.
		

A064460 Number of distinct nonsquarefree entries in n-th row of Pascal's triangle.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 1, 0, 3, 4, 3, 0, 5, 2, 2, 1, 8, 6, 9, 6, 7, 6, 6, 0, 11, 11, 10, 13, 13, 9, 13, 10, 16, 15, 14, 14, 18, 15, 13, 14, 19, 15, 15, 9, 15, 19, 14, 3, 24, 24, 25, 24, 24, 18, 26, 25, 28, 26, 25, 19, 27, 18, 12, 28, 32, 31, 31, 30, 31, 27, 30, 27, 36
Offset: 0

Views

Author

Robert G. Wilson v, Oct 02 2001

Keywords

Examples

			a(13) = 2 because C(13,5) = 3^2*11*13 and C(13,6) = 2^2*3*11*13.
		

Crossrefs

Programs

  • Mathematica
    f[ n_ ] := (c = 0; k = 1; While[ k < n/2 + .5, If[ Union[ Transpose[ FactorInteger[ Binomial[ n, k ] ] ] [ [ 2 ] ] ] [ [ -1 ] ] > 1, c++ ]; k++ ]; c); Table[ f[ n ], {n, 0, 100} ]
  • PARI
    a(n) = sum(k=0, n\2, !issquarefree(binomial(n, k))); \\ Michel Marcus, Mar 05 2014

Formula

a(n) + A238337(n) = A008619(n). - R. J. Mathar, Jan 18 2018

A064462 First row of Pascal's triangle that has n nonsquarefree entries, or -1 if no such row exists.

Original entry on oeis.org

0, 6, 4, 14, 13, 10, 8, -1, 9, 12, -1, 22, 17, 20, -1, 16, -1, 18, 29, 26, 31, 24, 25, 62, -1, 28, 27, 34, 35, 42, 33, 32, -1, -1, -1, 36, 53, 40, 45, -1, -1, -1, 95, -1, -1, -1, 79, 48, 49, 50, 55, 54, 57, 60, 69, 56, 63, 74, -1, 70, 67, 66, 65, 64, 77, -1
Offset: 0

Views

Author

Robert G. Wilson v, Oct 02 2001

Keywords

Comments

Numbers such that a(n) is -1: 7, 10, 14, 16, 24, 32, 33, 34, 39, 40, 41, 43, ... - Michel Marcus, Mar 05 2014

Examples

			a(4) = 13 because C(13,5) = C(13,8) = 3^2*11*13 and C(13,6) = C(13,7) = 2^2*3*11*13.
		

Crossrefs

Programs

  • Mathematica
    f[ n_ ] := (c = 0; k = 1; While[ k < n, If[ Union[ Transpose[ FactorInteger[ Binomial[ n, k ] ] ] [ [ 2 ] ] ] [ [ -1 ] ] > 1, c++ ]; k++ ]; c); Do[ m = 2; While[ f[ m ] != n, m++ ]; Print[ m ], {n, 0, 6} ]
  • PARI
    a(n, v) = {for (i=1, #v, if (v[i] == n, return (i-1));); return (-1);} \\ where v is vector A048277; Michel Marcus, Mar 05 2014

Extensions

Corrected and extended by Michel Marcus, Mar 05 2014

A238336 The first row of Pascal's triangle having exactly n distinct squarefree numbers, or -1 if no such row exists.

Original entry on oeis.org

0, 2, 5, 7, 13, 11, 15, 44, 53, 46, 59, 23, 43, 278, 191, 143, 79, 119, 187, 62, 47, 221, 214, 1643, 159, 238, 95, 473, 314, 3583, 671, 474, 958, 3071, 5719, 215, 1439, 7423, 1663, 447, 223, 3695, 4346, 4318, 12983, 319, 35069, 5983, 5471, 8567, 959, 3067
Offset: 1

Views

Author

T. D. Noe, Mar 05 2014

Keywords

Crossrefs

Programs

  • Mathematica
    nn = 20; t = Table[-1, {nn}]; found = 0; n = -1; While[found < nn, n++; len = Length[Select[Binomial[n, Range[0, n/2]], SquareFreeQ[#] &]]; If[0 < len <= nn && t[[len]] == -1, t[[len]] = n; found++]]; t

Extensions

Extended by T. D. Noe, Mar 07 2014
Showing 1-4 of 4 results.