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 1-5 of 5 results.

A126573 a(n) = sum of terms in n-th row of triangle A126571.

Original entry on oeis.org

1, 5, 12, 23, 36, 60, 78, 105, 132, 170, 201, 254, 290, 344, 397, 456, 502, 584, 637, 722, 793, 881, 946, 1057, 1131, 1233, 1320, 1437, 1516, 1679, 1770, 1892, 2002, 2140, 2254, 2425, 2529, 2675, 2808, 2984, 3100, 3322, 3448, 3621, 3785, 3971, 4108, 4339
Offset: 1

Views

Author

Leroy Quet, Dec 28 2006

Keywords

Crossrefs

Cf. A126571, A126574.

Programs

  • Mathematica
    f[m_, n_] := Block[{k = 0, c = n},While[c > 0,k++;While[GCD[k, m] > 1, k++ ];c--;];k];Table[Sum[f[m, n], {m, n}], {n, 50}] (* Ray Chandler, Dec 29 2006 *)

Extensions

Extended by Ray Chandler, Dec 29 2006

A126574 a(n) = product of terms in n-th row of triangle A126571.

Original entry on oeis.org

1, 6, 60, 980, 17010, 691152, 14385280, 553311000, 20549850750, 1183631840160, 40862208651264, 3546593581385400, 146387176845000000, 11600430026834880000, 876804182167691796480, 71417792752792726589856
Offset: 1

Views

Author

Leroy Quet, Dec 28 2006

Keywords

Crossrefs

Cf. A126571, A126573.

Programs

  • Mathematica
    f[m_, n_] := Block[{k = 0, c = n},While[c > 0,k++;While[GCD[k, m] > 1, k++ ];c--;];k];Table[Product[f[m, n], {m, n}], {n, 17}] (* Ray Chandler, Dec 29 2006 *)

Extensions

Extended by Ray Chandler, Dec 29 2006

A126575 a(n) = numerator of the sum of reciprocals of the terms in n-th row of triangle A126571.

Original entry on oeis.org

1, 5, 47, 103, 461, 21211, 24183, 62081, 735503, 38230051, 4501873, 40137823, 1571907737, 776878687, 13914337609, 13784887072529, 93498082849, 1626565056793, 25260167753, 213051987097, 15224249929987129
Offset: 1

Views

Author

Leroy Quet, Dec 28 2006

Keywords

Examples

			Row 4 of triangle A126571 is (4,7,5,7).
So a(4) is the numerator of 1/4 +1/7 +1/5 + 1/7 = 103/84.

Crossrefs

Cf. A126571, A126576.

Programs

  • Mathematica
    f[m_, n_] := Block[{k = 0, c = n},While[c > 0,k++;While[GCD[k, m] > 1, k++ ];c--;];k];Table[Numerator@Sum[1/f[m, n], {m, n}], {n, 22}] (* Ray Chandler, Dec 29 2006 *)

Extensions

Extended by Ray Chandler, Dec 29 2006

A126576 a(n) = denominator of the sum of reciprocals of the terms in n-th row of triangle A126571.

Original entry on oeis.org

1, 6, 60, 140, 630, 31416, 34580, 91080, 1093950, 58549260, 6702696, 61910940, 2379795600, 1197892080, 21742542360, 21741799002768, 143830236550, 2559047531040, 38886283310, 333903908520, 24063048428483064
Offset: 1

Views

Author

Leroy Quet, Dec 28 2006

Keywords

Examples

			Row 4 of triangle A126571 is (4,7,5,7).
So a(4) is the denominator of 1/4 +1/7 +1/5 + 1/7 = 103/84.

Crossrefs

Cf. A126571, A126575.

Programs

  • Mathematica
    f[m_, n_] := Block[{k = 0, c = n},While[c > 0,k++;While[GCD[k, m] > 1, k++ ];c--;];k];Table[Denominator@Sum[1/f[m, n], {m, n}], {n, 22}] (* Ray Chandler, Dec 29 2006 *)

Extensions

Extended by Ray Chandler, Dec 29 2006

A126572 Array read by antidiagonals: a(n,m) = the m-th integer from among those positive integers coprime to n.

Original entry on oeis.org

1, 1, 2, 1, 3, 3, 1, 2, 5, 4, 1, 3, 4, 7, 5, 1, 2, 5, 5, 9, 6, 1, 5, 3, 7, 7, 11, 7, 1, 2, 7, 4, 9, 8, 13, 8, 1, 3, 3, 11, 6, 11, 10, 15, 9, 1, 2, 5, 4, 13, 7, 13, 11, 17, 10, 1, 3, 4, 7, 5, 17, 8, 15, 13, 19, 11, 1, 2, 7, 5, 9, 6, 19, 9, 17, 14, 21, 12, 1, 5, 3, 9, 7, 11, 8, 23, 11, 19, 16, 23, 13
Offset: 1

Views

Author

Leroy Quet, Dec 28 2006

Keywords

Comments

From Rémy Sigrist, May 21 2017: (Start)
The n-th row only depends on the radical of n: a(n, m) = a(rad(n), m), where rad(n) = A007947(n).
The n-th row is linear: a(n, m + phi(rad(n))) = a(n, m) + rad(n), where phi(n) = A000010(n) and rad(n) = A007947(n).
(End)

Examples

			Array begins:
1,2,3,4,5,6,7,...
1,3,5,7,9,11,13,...
1,2,4,5,7,8,10,...
1,3,5,7,9,11,13,...
1,2,3,4,6,7,8,...
1,5,7,11,13,17,19,...
1,2,3,4,5,6,8,...
...

Crossrefs

Cf. A000010, A007947, A126571, A077581.

Programs

  • Mathematica
    f[m_, n_] := Block[{k = 0, c = n},While[c > 0,k++;While[GCD[k, m] > 1, k++ ];c--;];k];Flatten@Table[f[d - m + 1, m], {d, 13}, {m, d}] (* Ray Chandler, Dec 29 2006 *)

Extensions

Extended by Ray Chandler, Dec 29 2006
Showing 1-5 of 5 results.

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

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