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 1-2 of 2 results.

A336443 Primitive terms of A336442: terms k of A336442 such that none of the proper divisors of k are in A336442.

Original entry on oeis.org

60, 140, 210, 315, 462, 504, 616, 693, 728, 770, 792, 819, 910, 936, 990, 1001, 1092, 1144, 1170, 1287, 1430, 1530, 1683, 1716, 1870, 1989, 2090, 2142, 2145, 2210, 2244, 2431, 2448, 2470, 2508, 2618, 2652, 2717, 2805, 2926, 2964, 2992, 3094, 3135, 3230, 3315
Offset: 1

Views

Author

Amiram Eldar, Jul 21 2020

Keywords

Comments

Any term of A336442 is a multiple of at least one term of this sequence.

Examples

			60 is a term since it is a term of A336442 but none of its proper divisors are in A336442.
120 is not a term: although it is in A336442, it is a multiple of 60 which is also a term of A336442.

Links

Crossrefs

Analogous to A302022 as A336442 is analogous to A005279.

Programs

  • Mathematica
    divQ[n_] := AnyTrue[Subsets[Divisors[n], {3}], And @@ CoprimeQ @@@ Subsets[#, {2}] && #[[3]] < 2 #[[1]] &]; primQ[n_] := divQ[n] && AllTrue[Most[Divisors[n]], ! divQ[#] &]; Select[Range[3333], primQ]

A302296 Positive numbers that can be written in exactly one way as i*j*k with i < j < 2*i.

Original entry on oeis.org

6, 15, 18, 20, 28, 35, 63, 75, 77, 78, 88, 91, 99, 100, 102, 104, 110, 114, 117, 130, 138, 143, 153, 170, 174, 175, 186, 187, 189, 190, 196, 209, 221, 222, 238, 245, 246, 247, 258, 266, 272, 282, 297, 299, 304, 318, 322, 323, 325, 351, 354, 357, 366, 368, 391, 399, 402, 425, 426, 429, 437, 438
Offset: 1

Views

Author

Robert Israel, Apr 04 2018

Keywords

Comments

Numbers n such that A301989(n)=1.

Examples

			a(5)=28 is in the sequence because 28 = 4*7*1 is the only way to write 28=i*j*k with i < j < 2*i.

Links

Crossrefs

Cf. A301989, A302022.

Programs

  • Maple
    N:= 1000: # to get all terms <= N
V:= Vector(N):
for i from 1 to isqrt(N-1) do
  for j from i+1 to min(floor(N/i),2*i-1) do
    for k from 1 to floor(N/(i*j)) do
      n:= i*j*k;
      V[n]:= V[n]+1;
od od od:
select(t -> V[t]=1, [$1..N]);
  • Mathematica
    M = 1000;
V = Table[0, {M}];
For[i = 1, i <= Sqrt[M-1], i++,
  For[j = i+1, j <= Min[Floor[M/i], 2i-1], j++,
    For[k = 1, k <= Floor[M/(i j)], k++,
      n = i j k;
      V[[n]] = V[[n]]+1;
]]];
Position[V, 1] // Flatten (* Jean-François Alcover, Apr 29 2019, after Robert Israel *)
  • PARI
    list(lim)=my(v=List(),u=vectorsmall(lim\=1),t); for(i=1, sqrtint(lim), for(j=i+1,min(lim\i,2*i-1), t=i*j; forstep(n=t,lim,t, u[n]++))); for(i=1,#u, if(u[i]==1, listput(v,i))); Vec(v) \\ Charles R Greathouse IV, Apr 05 2018
Showing 1-2 of 2 results.

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

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