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.

A106502 Shortest side of primitive integer-sided triangle having an angle twice another, sorted on perimeter (A106499).

Original entry on oeis.org

4, 7, 9, 9, 11, 16, 24, 13, 25, 15, 25, 32, 17, 49, 36, 19, 49, 57, 40, 49, 21, 49, 64, 23, 81, 69, 48, 81, 25, 64, 75, 27, 104, 81, 56, 121, 29, 81, 100, 87, 121, 144, 31, 120, 121, 93, 64, 100, 155, 33, 121, 144, 169, 121, 165, 35, 136, 169, 105, 121, 72, 37, 169, 111, 169
Offset: 1

Views

Author

Lekraj Beedassy, May 04 2005

Keywords

Comments

Triple is (A106502,106503,106504).

Crossrefs

Cf. A106499-A106506, A106410, A106420, A106430.

Extensions

Corrected and extended by Ray Chandler, May 09 2005

A302022 Primitive terms from A005279.

Original entry on oeis.org

6, 15, 20, 28, 35, 63, 77, 88, 91, 99, 104, 110, 117, 130, 143, 153, 170, 187, 190, 209, 221, 238, 247, 266, 272, 299, 304, 322, 323, 325, 357, 368, 391, 399, 425, 437, 464, 475, 483, 493, 496, 506, 513, 527, 551, 575, 589, 609, 621, 638, 651, 667, 682, 703, 713, 725, 754, 759, 775, 777, 783, 806, 814
Offset: 1

Views

Author

David A. Corneth, Mar 31 2018

Keywords

Comments

Also numbers k such that k is in A005279 but none of the proper divisors of k are.
All terms k are composites; if k is prime then it's not in A005279 hence not here. If k = m * t and t < m < 2*t then m and t are coprime. If g = gcd(t, m) > 1 then the integer k / g^2 is in A005279. If there is some term u*t where with u > 2*t and gcd(u, t) = 1 then there is some m * t' with gcd(m, t') = 1 such that m*t' | t * u and t * u wouldn't be in the sequence. if u = 2*t then gcd(u, t) = t which can't happen.
It could be that both m and t are composite, for example, t = 53^2 and m = 5^5 gives the term 53^2 * 5^5.
Interestingly, k = m * t where t < m < 2 * t and m * t is in A005279 and m, t coprime gives A106430; this sequence is a subsequence of A106430.

Examples

			77 is a term since it is in A005279 and 77 is not of the form A005279(i)*t for t > 1.

Links

Crossrefs

Subsequence of A020886 and hence of A005279.
Cf. A106430, A301989, A302296.

Programs

  • PARI
    is005279(n) = my(d=divisors(n)); for(i=3, #d, if(d[i]<2*d[i-1], return(1))); 0;
is(n) = if (is005279(n), d = divisors(n); for (k=1, #d-1, if (is005279(d[k]), return (0));); return(1);); \\ Altug Alkan, Apr 14 2018
upto(n) = {my(res = List()); for(i = 2, sqrtint(n), for(j = i+1, min(2 * i - 1, n\i), if(gcd(i, j) == 1, if(is(i*j), listput(res, i*j))))); listsort(res); return(res)} \\ David A. Corneth, Apr 15 2018

Formula

A301989(a(n)) = 1.

A106503 Middle side of primitive integer-sided triangle having an angle twice another, sorted on perimeter (A106499).

Original entry on oeis.org

5, 9, 15, 16, 25, 28, 25, 36, 39, 49, 45, 49, 64, 51, 66, 81, 72, 64, 81, 84, 100, 91, 104, 121, 88, 100, 121, 115, 144, 120, 121, 169, 121, 144, 169, 135, 196, 153, 170, 169, 168, 145, 225, 169, 198, 196, 225, 190, 169, 256, 209, 217, 192, 220, 196, 289, 225, 231
Offset: 1

Views

Author

Lekraj Beedassy, May 04 2005

Keywords

Comments

Triple is (A106502, A106503, A106504).

Crossrefs

Cf. A106499-A106506, A106410, A106420, A106430.

Extensions

Corrected and extended by Ray Chandler, May 09 2005

A106504 Longest side of primitive integer-sided triangle having an angle twice another, sorted on perimeter (A106499).

Original entry on oeis.org

6, 12, 16, 20, 30, 33, 35, 42, 40, 56, 56, 63, 72, 70, 85, 90, 77, 88, 99, 95, 110, 120, 105, 132, 117, 130, 143, 126, 156, 161, 154, 182, 165, 175, 195, 176, 210, 208, 189, 208, 187, 204, 240, 221, 203, 238, 255, 261, 234, 272, 240, 228, 247, 279, 266, 306, 285
Offset: 1

Views

Author

Lekraj Beedassy, May 04 2005

Keywords

Comments

Triple is (A106502, A106503, A106504).

Links

Crossrefs

Cf. A106499-A106506, A106410, A106420, A106430.

Extensions

Corrected and extended by Ray Chandler, May 09 2005

A280680 The square roots of the radii (a, b, c) of three primitive mutually tangent circles all touching the same straight line, with a > b > c.

Original entry on oeis.org

6, 3, 2, 12, 4, 3, 15, 10, 6, 20, 5, 4, 28, 21, 12, 30, 6, 5, 35, 14, 10, 40, 24, 15, 42, 7, 6, 45, 36, 20, 56, 8, 7, 63, 18, 14, 66, 55, 30, 70, 30, 21, 72, 9, 8, 77, 44, 28, 84, 60, 35, 88, 33, 24, 90, 10, 9, 91, 78, 42, 99, 22, 18, 104, 65, 40
Offset: 1

Views

Author

Colin Barker, Jan 07 2017

Keywords

Examples

			The first few triples are [6, 3, 2], [12, 4, 3], [15, 10, 6], [20, 5, 4].

Links

Crossrefs

Cf. A106430, A246429, A247372, A265189, A280679.

Programs

  • PARI
    a280680(amax) = {
  my(L=List());
  for(a=1, amax,
    for(b=1, a-1,
      c=(1/(1/a + 1/b))^2;
      if(type(c)=="t_INT" && gcd([a^2,b^2,c])==1,
        listput(L, [a,b,sqrtint(c)])
      )
    )
  );
  Vec(L)
}
concat(a280680(100))
Previous Showing 11-15 of 15 results.

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

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