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.

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A176172 3rd prime-factor of n-th product of 4 distinct primes.

Original entry on oeis.org

5, 5, 5, 7, 5, 7, 5, 5, 7, 7, 7, 11, 5, 7, 5, 7, 5, 11, 7, 7, 7, 5, 11, 5, 7, 13, 7, 7, 5, 11, 13, 11, 7, 5, 7, 7, 5, 7, 13, 7, 5, 11, 11, 17, 7, 7, 11, 5, 7, 11, 11, 5, 11, 7, 5, 13, 7, 13, 17, 5, 7, 13, 11, 13, 7, 5, 11, 7, 7, 11, 19, 5, 11, 11, 7, 11, 7, 13, 5, 11, 17, 7, 13, 11, 7, 5, 7, 7, 5
Offset: 1

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Author

Keywords

Comments

FactorInteger[210]=2*3*5*7,...

Crossrefs

Programs

  • Maple
    N:= 10000: # to use products <= N
    Primes:= select(isprime, [2,seq(i,i=3..N/30)]):
    P4:= NULL:
    for ia from 1 to nops(Primes) do
      a:= Primes[ia];
      for ib from 1 to ia-1 do
        b:= Primes[ib];
        if 6*a*b > N then break fi;
        for ic from 1 to ib-1 do
          c:= Primes[ic];
          if 2*a*b*c > N then break fi;
          for id from 1 to ic-1 do
            d:= Primes[id];
            if a*b*c*d > N then break fi;
            R[a*b*c*d]:= b;
            P4:= P4, a*b*c*d;
    od od od od:
    P4:= sort([P4]):
    map(t -> R[t], P4); # Robert Israel, May 14 2019
  • Mathematica
    f0[n_]:=Last/@FactorInteger[n]=={1,1,1,1};f1[n_]:=Min[First/@FactorInteger[n]];f2[n_]:=First/@FactorInteger[n][[2,1]];f3[n_]:=First/@FactorInteger[n][[3,1]];f4[n_]:=Max[First/@FactorInteger[n]];lst={};Do[If[f0[n],AppendTo[lst,f3[n]]],{n,0,2*7!}];lst

A176173 4th|largest prime-factor of n-th product of 4 distinct primes.

Original entry on oeis.org

7, 11, 13, 11, 17, 13, 19, 23, 17, 11, 19, 13, 29, 13, 31, 23, 37, 17, 11, 17, 29, 41, 19, 43, 31, 17, 19, 13, 47, 13, 19, 23, 37, 53, 23, 41, 59, 17, 23, 43, 61, 17, 29, 19, 47, 19, 13, 67, 29, 31, 19, 71, 13, 31, 73, 17, 53, 29, 23, 79, 23, 31, 37, 19, 59, 83, 23, 61, 37, 17
Offset: 1

Views

Author

Keywords

Comments

FactorInteger[210]=2*3*5*7,...

Crossrefs

Programs

  • Mathematica
    f0[n_]:=Last/@FactorInteger[n]=={1,1,1,1};f1[n_]:=Min[First/@FactorInteger[n]];f2[n_]:=First/@FactorInteger[n][[2,1]];f3[n_]:=First/@FactorInteger[n][[3,1]];f4[n_]:=Max[First/@FactorInteger[n]];lst={};Do[If[f0[n],AppendTo[lst,f4[n]]],{n,0,2*7!}];lst

A343004 Pairwise listing of the prime factors of the squarefree semiprimes (smaller, larger).

Original entry on oeis.org

2, 3, 2, 5, 2, 7, 3, 5, 3, 7, 2, 11, 2, 13, 3, 11, 2, 17, 5, 7, 2, 19, 3, 13, 2, 23, 3, 17, 5, 11, 3, 19, 2, 29, 2, 31, 5, 13, 3, 23, 2, 37, 7, 11, 2, 41, 5, 17, 2, 43, 3, 29, 7, 13, 3, 31, 2, 47, 5, 19, 2, 53, 3, 37, 5, 23, 2, 59, 7, 17, 2, 61, 3, 41, 3, 43, 7, 19, 2, 67, 3, 47, 2, 71, 11, 13, 5, 29
Offset: 1

Views

Author

Wesley Ivan Hurt, Apr 28 2021

Keywords

Comments

Interspersion of A096916 and A070647.

Examples

			The first squarefree semiprime is 6 = 2*3.  Therefore a(1) = 2 and a(2) = 3.
		

Crossrefs

Cf. A006881, A096916 and A070647 (lesser and larger prime factors).

Programs

  • Mathematica
    Flatten@ Map[FactorInteger[#][[All, 1]] &, Select[Range[6, 150], And[PrimeOmega[#] == 2, SquareFreeQ[#]] &]] (* or *)
    Block[{nn = 35, a = {}, lim}, lim = Prime[nn]; Do[Do[If[#3 <= lim, AppendTo[a, {#3, #2, #1}], Break[]] & @@ {#1, #2, #1 #2} & @@ {Prime[i], Prime[j]}, {i, j + 1, nn}], {j, nn}]; Flatten@ Sort[a][[All, 2 ;; 3]]] (* Michael De Vlieger, May 01 2021 *)
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