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 1-3 of 3 results.

A279453 Triangle read by rows: T(n, k) is the number of nonequivalent ways to place k points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 1, 3, 8, 14, 17, 9, 2, 1, 3, 21, 73, 202, 306, 285, 115, 20, 1, 6, 49, 301, 1397, 4361, 9110, 11810, 8679, 2929, 288, 1, 6, 93, 890, 6582, 34059, 126396, 326190, 568134, 624875, 390426, 111798, 8791, 1, 10, 171, 2321, 24185, 185181, 1055025
Offset: 1

Views

Author

Heinrich Ludwig, Dec 17 2016

Keywords

Comments

Length of n-th row is A272651(n) + 1, where A272651(n) is the maximal number of points that can be placed under the condition mentioned.
Rotations and reflections of placements are not counted. If they are to be counted, see A279445.
For condition "no more than 2 points on a straight line at any angle", see A235453.

Examples

			The table begins with T(1, 0):
1 1
1 1  2   1    1
1 3  8  14   17    9    2
1 3 21  73  202  306  285   115   20
1 6 49 301 1397 4361 9110 11810 8679 2929 288
...
T(4, 3) = 73 because there are 73 nonequivalent ways to place 3 points on a 4 X 4 square grid so that no more than 2 points are on a vertical or horizontal straight line.

Links

Crossrefs

Row sums give A279454.
Columns 2..8: A008805, A014409, A279454, A279455, A279456, A279457, A279458.
Diagonal T(n, n) is A279452.
Cf. A279445, A235453.

A279456 Numbers k such that number of distinct primes dividing k is odd and number of prime divisors (counted with multiplicity) of k is even.

Original entry on oeis.org

4, 9, 16, 25, 49, 60, 64, 81, 84, 90, 121, 126, 132, 140, 150, 156, 169, 198, 204, 220, 228, 234, 240, 256, 260, 276, 289, 294, 306, 308, 315, 336, 340, 342, 348, 350, 360, 361, 364, 372, 380, 414, 444, 460, 476, 490, 492, 495, 504, 516, 522, 525, 528, 529, 532, 540, 550, 558, 560, 564, 572, 580, 585, 600
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 12 2016

Keywords

Comments

Intersection of A028260 and A030230.
Numbers k such that A000035(A001221(k)) = 1 and A000035(A001222(k)) = 0.
Numbers k such that A076479(k) = -1 and A008836(k) = 1.

Examples

			90 is in the sequence because 90 = 2*3^2*5 therefore omega(90) = 3 {2,3,5} is odd and bigomega(90) = 4 {2,3,3,5} is even.

Links

Crossrefs

Cf. A000035, A001221, A001222, A008836, A028260, A030230, A076479, A082522 (subsequence), A187039, A279457, A279458.

Programs

  • Mathematica
    Select[Range[600], Mod[PrimeNu[#1], 2] == 1 && Mod[PrimeOmega[#1], 2] == 0 & ]
  • PARI
    is(k) = {my(f = factor(k)); omega(f) % 2 && !(bigomega(f) % 2);} \\ Amiram Eldar, Sep 17 2024

A279458 Numbers k such that number of distinct primes dividing k is even and number of prime divisors (counted with multiplicity) of k is even.

Original entry on oeis.org

1, 6, 10, 14, 15, 21, 22, 24, 26, 33, 34, 35, 36, 38, 39, 40, 46, 51, 54, 55, 56, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 88, 91, 93, 94, 95, 96, 100, 104, 106, 111, 115, 118, 119, 122, 123, 129, 133, 134, 135, 136, 141, 142, 143, 144, 145, 146, 152, 155, 158, 159, 160, 161, 166, 177, 178, 183, 184, 185, 187, 189
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 12 2016

Keywords

Comments

Intersection of A028260 and A030231.
Numbers k such that A000035(A001221(k)) = 0 and A000035(A001222(k)) = 0.
Numbers k such that A076479(k) = 1 and A008836(k) = 1.

Examples

			24 is in the sequence because 24 = 2^3*3 therefore omega(24) = 2 {2,3} is even and bigomega(24) = 4 {2,2,2,3} is even.

Links

Crossrefs

Cf. A000035, A001221, A001222, A008836, A028260, A030231, A076479, A279456, A279457.

Programs

  • Mathematica
    Select[Range[220], Mod[PrimeNu[#1], 2] == Mod[PrimeOmega[#1], 2] == 0 & ]
  • PARI
    is(k) = {my(f = factor(k)); !(omega(f) % 2) && !(bigomega(f) % 2);} \\ Amiram Eldar, Sep 17 2024
Showing 1-3 of 3 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.