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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.

A114718 a(n) = sum of terms in n-th row of triangle A112599.

Original entry on oeis.org

1, 2, 6, 6, 10, 13, 17, 43, 59, 69, 85, 85, 103, 123, 147, 128, 185, 171, 246, 192, 259, 224, 356, 328, 400, 358, 373, 498, 497, 496, 787, 443, 886, 664, 560, 795, 770, 839, 945, 993, 981, 866, 1083, 1010, 1449, 1173, 1439, 1400, 1656, 1389, 1380, 1526, 1445
Offset: 1

Views

Author

Leroy Quet, Dec 27 2005

Keywords

Examples

			The 7th row of triangle A112599 is [6,1,3,1,2,1,3]. So a(7) = 6+1+3+1+2+1+3 = 17.

Crossrefs

Cf. A112599, A114719.

Programs

  • Mathematica
    f[l_] := Block[{p, t}, p = l[[ -1]]; k = Length@p; t = Table[ Count[ GCD[p, n], 1], {n, k + 1}]; Return@Append[l, t];]; Plus @@@ Nest[f, {{1}}, 52] (* Robert G. Wilson v *)

Extensions

More terms from Robert G. Wilson v, Dec 28 2005

A112631 Rightmost term of each row of triangle A112599. (For n >= 2, a(n) = number of terms in the (n-1)th row of triangle A112599 which are coprime to n.)

Original entry on oeis.org

1, 1, 2, 0, 2, 0, 3, 5, 7, 5, 10, 4, 12, 9, 6, 5, 16, 3, 18, 2, 17, 5, 22, 8, 22, 12, 13, 8, 28, 5, 30, 5, 30, 15, 22, 9, 36, 23, 18, 16, 40, 2, 42, 15, 20, 9, 46, 20, 46, 12, 23, 21, 52, 10, 33, 26, 40, 27, 58, 21, 60, 23, 41, 31, 55, 11, 66, 32, 44, 21, 70, 19, 72, 23, 40, 28, 63, 17
Offset: 1

Views

Author

Leroy Quet, Dec 22 2005

Keywords

Comments

It appears that there are no 0's in A112599 after the 6th row. If so, a(p) = p-1 for every prime p except 5 and 7. - Franklin T. Adams-Watters, Nov 15 2006

Examples

			The 6th row of triangle A112599 is [5,0,4,0,4,0]. So a(7) is the number of these terms which are coprime to 7. Now 5, 4 and 4 are coprime to 7, but the 0's are not; so a(7) = 3.

Crossrefs

Cf. A112599, A112635.

Extensions

More terms from Franklin T. Adams-Watters, Nov 15 2006

A112592 Triangle where a(1,1) = 0, a(n,m) = number of terms of row (n-1) which are coprime to m.

Original entry on oeis.org

0, 1, 0, 2, 1, 1, 3, 2, 3, 2, 4, 2, 2, 2, 4, 5, 0, 5, 0, 5, 0, 6, 3, 3, 3, 0, 3, 3, 7, 5, 0, 5, 6, 0, 6, 5, 8, 4, 4, 4, 3, 4, 5, 4, 4, 9, 2, 8, 2, 8, 1, 9, 2, 8, 1, 10, 4, 8, 4, 10, 2, 10, 4, 8, 4, 10, 11, 0, 11, 0, 7, 0, 11, 0, 11, 0, 11, 0, 12, 6, 6, 6, 6, 6, 5, 6, 6, 6, 1, 6, 6, 13, 2, 2, 2, 12, 2, 13, 2
Offset: 1

Views

Author

Leroy Quet, Dec 24 2005

Keywords

Comments

GCD(m,0) is considered here to be m, so 0 is coprime to no positive integer but 1.

Examples

			Row 6 of the triangle is [5,0,5,0,5,0]. Among these terms there are 6 terms coprime to 1, 3 terms coprime to 2, 3 terms coprime to 3, 3 terms coprime to 4, 0 terms coprime to 5, 3 terms coprime to 6 and 3 terms coprime to 7. So row 7 is [6,3,3,3,0,3,3].
0,
1,0,
2,1,1,
3,2,3,2,
4,2,2,2,4,
5,0,5,0,5,0,
6,3,3,3,0,3,3,
7,5,0,5,6,0,6,5,
8,4,4,4,3,4,5,4,4

Links

Crossrefs

Cf. A112599.
Row sums are in A114719. [From Klaus Brockhaus, Jun 01 2009]

Programs

  • Mathematica
    f[l_] := Block[{p, t}, p = l[[ -1]]; k = Length@p; t = Table[Count[GCD[p, n], 1], {n, k + 1}]; Return@Append[l, t];]; Nest[f, {{0}}, 13] // Flatten (* Robert G. Wilson v *)

Extensions

More terms from Robert G. Wilson v, Dec 27 2005
Terms a(100) through a(2000) from Diana L. Mecum, Aug 12 2008

A112593 Triangle where a(1,1) = 1, a(n,m) = number of terms of row (n-1) which are coprime to m. Row n has (2n-1) terms.

Original entry on oeis.org

1, 1, 1, 1, 3, 3, 3, 3, 3, 5, 5, 0, 5, 5, 0, 5, 7, 5, 5, 5, 0, 5, 5, 5, 5, 9, 8, 8, 8, 1, 8, 7, 8, 8, 1, 8, 11, 4, 10, 4, 11, 3, 10, 4, 10, 4, 11, 3, 11, 13, 6, 11, 6, 10, 4, 13, 6, 11, 6, 9, 4, 13, 6, 8, 15, 6, 9, 6, 14, 5, 15, 6, 9, 6, 13, 5, 12, 6, 8, 6, 15, 17, 8, 5, 8, 12, 3, 16, 8, 5, 3, 17, 3, 16
Offset: 1

Views

Author

Leroy Quet, Dec 24 2005

Keywords

Comments

GCD(m,0) is considered here to be m, so 0 is coprime to no positive integer but 1.

Examples

			Row 5 of the triangle is [7,5,5,5,0,5,5,5,5].
Among these terms there are 9 terms coprime to 1, 8 terms coprime to 2, 8 terms coprime to 3, 8 terms coprime to 4, 1 term coprime to 5, 8 terms coprime to 6, 7 terms coprime to 7, 8 terms coprime to 8, 8 terms coprime to 9, 1 term coprime to 10 and 8 terms coprime to 11. So row 6 is [9,8,8,8,1,8,7,8,8,1,8].
Table begins:
1,
1,1,1,
3,3,3,3,3,
5,5,0,5,5,0,5,
7,5,5,5,0,5,5,5,5,
9,8,8,8,1,8,7,8,8,1,8,
11,4,10,4,11,3,10,4,10,4,11,3,11,
13,6,11,6,10,4,13,6,11,6,9,4,13,6,8,
15,6,9,6,14,5,15,6,9,6,13,5,12,6,8,6,15,
17,8,5,8,12,3,16,8,5,3,17,3,16,8,3,8,17,3,17

Crossrefs

Cf. A112599.
Row sums are in A160991. [From Klaus Brockhaus, Jun 01 2009]

Programs

  • Mathematica
    f[l_] := Append[l, Table[ Count[GCD[Last[l], n], 1], {n, Length[Last[l]] + 2}]]; Flatten[Nest[f, {{1}}, 9]] (* Ray Chandler, Jan 02 2006 *)
t[1, 1] = 1; t[n_, m_] := t[n, m] = Count[ GCD[ Table[ t[n - 1, k], {k, 2n - 3}], m], 1]; Table[ t[n, m], {n, 10}, {m, 2n - 1}] // Flatten (* Robert G. Wilson v *)
  • PARI
    {print1(s=1,",");v=[s];for(i=2,10,w=vector(2*i-1);for(j=1,2*i-1,c=0;for(k=1,2*i-3,if(gcd(v[k],j)==1,c++));print1(w[j]=c,","));v=w)} (Brockhaus)

Extensions

More terms from Robert G. Wilson v, Klaus Brockhaus and Ray Chandler, Jan 02 2006
Showing 1-4 of 4 results.

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