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 11-15 of 15 results.

A258859 Ninth pi-based arithmetic derivative of n.

Original entry on oeis.org

0, 0, 0, 0, 4, 0, 4, 4, 81920, 81920, 0, 0, 622592, 4, 512, 2304, 4931584, 4, 2304, 12288, 4931584, 512, 208, 12288, 193644, 12288, 2304, 8322048, 423168, 0, 81920, 0, 38944768, 12288, 0, 4, 37880, 81920, 4, 423168, 37880, 4, 80, 208, 2298880, 43632, 4, 512
Offset: 0

Views

Author

Alois P. Heinz, Jun 12 2015

Keywords

Links

Crossrefs

Column k=9 of A258850.
Cf. A000720, A258851.

Programs

  • Maple
    with(numtheory):
d:= n-> n*add(i[2]*pi(i[1])/i[1], i=ifactors(n)[2]):
A:= proc(n, k) option remember; `if`(k=0, n, d(A(n, k-1))) end:
a:= n-> A(n, 9):
seq(a(n), n=0..100);

Formula

a(n) = A258851^9(n).

A258860 Tenth pi-based arithmetic derivative of n.

Original entry on oeis.org

0, 0, 0, 0, 4, 0, 4, 4, 622592, 622592, 0, 0, 4931584, 4, 2304, 12288, 38944768, 4, 12288, 81920, 38944768, 2304, 512, 81920, 714096, 81920, 12288, 65719296, 2298880, 0, 622592, 0, 278380544, 81920, 0, 4, 85988, 622592, 4, 2298880, 85988, 4, 208, 512, 13319168
Offset: 0

Views

Author

Alois P. Heinz, Jun 12 2015

Keywords

Links

Crossrefs

Column k=10 of A258850.
Cf. A000720, A258851.

Programs

  • Maple
    with(numtheory):
d:= n-> n*add(i[2]*pi(i[1])/i[1], i=ifactors(n)[2]):
A:= proc(n, k) option remember; `if`(k=0, n, d(A(n, k-1))) end:
a:= n-> A(n, 10):
seq(a(n), n=0..100);

Formula

a(n) = A258851^10(n).

A258975 a(n) = n-th pi-based antiderivative of 1.

Original entry on oeis.org

1, 2, 3, 5, 11, 10, 29, 78, 141, 266, 147, 194, 1181, 2413, 1834, 6293, 4805, 20290, 28345, 25065, 85334, 87967, 55722, 191559, 385845, 437914, 998758, 396375, 95625, 202043, 341774, 2217782, 1607613, 1333107, 1697893, 1222517, 2277354, 1599111
Offset: 0

Views

Author

Alois P. Heinz, Jun 18 2015

Keywords

Examples

			a(6) = 29 -> 10 -> 11 -> 5 -> 3 -> 2 -> 1.
a(7) = 78 -> 127 -> 31 -> 11 -> 5 -> 3 -> 2 -> 1.

Crossrefs

Row n=1 of A259016.
Cf. A000720, A258850, A258851.

Formula

a(n) = min { m >= 0 : A258851^n(m) = 1 }.
A258850(a(n),n) = 1.

A258847 Sum of the k-th pi-based arithmetic derivative of n-k for k=0..n.

Original entry on oeis.org

0, 1, 2, 4, 6, 10, 13, 20, 21, 33, 54, 86, 146, 339, 788, 2947, 14870, 94801, 706961, 5566784, 43958933, 317950465, 2406052444, 19645433193, 146175038733, 1479263447899, 16135114175706, 203382520812382, 2606355260220040, 32974597626726301, 406609097787758227
Offset: 0

Views

Author

Alois P. Heinz, Jun 12 2015

Keywords

Crossrefs

Antidiagonal sums of A258850.
Cf. A000720, A258851.

Programs

  • Maple
    with(numtheory):
d:= n-> n*add(i[2]*pi(i[1])/i[1], i=ifactors(n)[2]):
A:= proc(n, k) option remember; `if`(k=0, n, d(A(n, k-1))) end:
a:= proc(n) option remember; add(A(h, n-h), h=0..n) end:
seq(a(n), n=0..30);

Formula

a(n) = Sum_{k=0..n} A258850(n-k,k).

A258849 The n-th pi-based arithmetic derivative of n.

Original entry on oeis.org

0, 0, 0, 0, 4, 0, 4, 4, 12288, 81920, 0, 0, 278380544, 4, 4931584, 278380544, 14768867966976, 4, 128412352512, 14768867966976, 375877192068366336, 14768867966976, 14768867966976, 375877192068366336
Offset: 0

Views

Author

Alois P. Heinz, Jun 12 2015

Keywords

Crossrefs

Main diagonal of A258850.
Cf. A000720, A258851.

Programs

  • Maple
    with(numtheory):
d:= n-> n*add(i[2]*pi(i[1])/i[1], i=ifactors(n)[2]):
A:= proc(n, k) option remember; `if`(k=0, n, d(A(n, k-1))) end:
a:= n-> A(n$2):
seq(a(n), n=0..23);

Formula

a(n) = A258851^n(n) = A258850(n,n).
Previous Showing 11-15 of 15 results.

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

Content is available under The OEIS End-User License Agreement.