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.

A368611 a(n) = Sum_{k=1..n} pi(k) * floor(n/k).

Original entry on oeis.org

0, 1, 3, 6, 9, 15, 19, 26, 32, 40, 45, 58, 64, 75, 86, 99, 106, 123, 131, 149, 163, 177, 186, 212, 224, 240, 255, 277, 287, 316, 327, 351, 369, 388, 406, 441, 453, 474, 494, 528, 541, 578, 592, 622, 651, 675, 690, 737, 756, 788, 812, 845, 861, 903, 927, 969, 995, 1022
Offset: 1

Views

Author

Wesley Ivan Hurt, Dec 31 2023

Keywords

Crossrefs

Cf. A000720 (pi), A013939, A046992, A368610, A368612, A368613.

Programs

  • Mathematica
    Table[Sum[PrimePi[k] Floor[n/k], {k, n}], {n, 100}]

Formula

a(n) = A013939(n) + A368613(n).

A368612 a(n) = Sum_{k=2..n} pi(k-1) * ceiling(n/k).

Original entry on oeis.org

0, 0, 1, 4, 8, 13, 20, 27, 37, 46, 56, 65, 81, 92, 107, 122, 140, 153, 175, 190, 214, 234, 254, 271, 304, 324, 347, 370, 399, 418, 454, 475, 509, 536, 564, 591, 635, 658, 689, 719, 763, 788, 835, 862, 904, 945, 981, 1010, 1070, 1103, 1148, 1185, 1231, 1262, 1318, 1356
Offset: 1

Views

Author

Wesley Ivan Hurt, Dec 31 2023

Keywords

Crossrefs

Cf. A000720 (pi), A046992, A092494, A368610, A368611, A368613.

Programs

  • Mathematica
    Table[Sum[PrimePi[k - 1] Ceiling[n/k], {k, 2, n}], {n, 100}]

Formula

a(n) = A368610(n) - A092494(n).

A368613 a(n) = Sum_{k=2..n} pi(k-1) * floor(n/k).

Original entry on oeis.org

0, 0, 1, 3, 5, 9, 12, 18, 23, 29, 33, 44, 49, 58, 67, 79, 85, 100, 107, 123, 135, 147, 155, 179, 190, 204, 218, 238, 247, 273, 283, 306, 322, 339, 355, 388, 399, 418, 436, 468, 480, 514, 527, 555, 582, 604, 618, 663, 681, 711, 733, 764, 779, 819, 841, 881, 905, 930
Offset: 1

Views

Author

Wesley Ivan Hurt, Dec 31 2023

Keywords

Crossrefs

Cf. A000720 (pi), A013939, A046992, A368610, A368611, A368612.

Programs

  • Mathematica
    Table[Sum[PrimePi[k - 1] Floor[n/k], {k, 2, n}], {n, 100}]

Formula

a(n) = A368611(n) - A013939(n).

A368616 a(n) = Sum_{k=1..n} pi(k) * (ceiling(n/k) - floor(n/k)).

Original entry on oeis.org

0, 0, 1, 2, 5, 5, 11, 12, 17, 19, 27, 24, 37, 38, 44, 48, 61, 58, 75, 73, 85, 93, 107, 99, 122, 127, 137, 139, 161, 152, 181, 179, 196, 206, 218, 212, 247, 250, 263, 261, 295, 284, 321, 319, 334, 353, 377, 360, 403, 405, 428, 434, 467, 457, 491, 489, 521, 536, 563, 536, 597, 603, 615
Offset: 1

Views

Author

Wesley Ivan Hurt, Dec 31 2023

Keywords

Crossrefs

Cf. A000720 (pi), A024816, A046992, A048865, A049820, A062774, A368610, A368611, A368641.

Programs

  • Mathematica
    Table[Sum[PrimePi[k] (Ceiling[n/k] - Floor[n/k]), {k, n}], {n, 100}]

Formula

a(n) = A368610(n) - A368611(n).
a(n) = A046992(n) - A062774(n).
a(n) = A368641(n) + A048865(n).

A368641 a(n) = Sum_{k=2..n} pi(k-1) * (ceiling(n/k) - floor(n/k)).

Original entry on oeis.org

0, 0, 0, 1, 3, 4, 8, 9, 14, 17, 23, 21, 32, 34, 40, 43, 55, 53, 68, 67, 79, 87, 99, 92, 114, 120, 129, 132, 152, 145, 171, 169, 187, 197, 209, 203, 236, 240, 253, 251, 283, 274, 308, 307, 322, 341, 363, 347, 389, 392, 415, 421, 452, 443, 477, 475, 507, 522, 547, 522
Offset: 1

Views

Author

Wesley Ivan Hurt, Jan 01 2024

Keywords

Crossrefs

Cf. A000720 (pi), A046992, A048865, A092494, A368610, A368611, A368612, A368613, A368616.

Programs

  • Mathematica
    Table[Sum[PrimePi[k - 1] (Ceiling[n/k] - Floor[n/k]), {k, 2, n}], {n, 100}]

Formula

a(n) = A368612(n) - A368613(n).
a(n) = A368616(n) - A048865(n).
Showing 1-5 of 5 results.

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