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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 1-4 of 4 results.

A264762 a(n) is the index of A246946(n) in A024619, integers x that satisfy omega(x) >= 2.

Original entry on oeis.org

1, 3, 6, 10, 13, 2, 7, 20, 26, 34, 5, 23, 44, 55, 17, 21, 4, 12, 31, 41, 16, 67, 8, 36, 50, 25, 29, 38, 9, 22, 54, 70, 30, 113, 14, 63, 86, 42, 47, 11, 28, 66, 85, 37, 136, 19, 76, 106, 61, 65, 15, 39, 90, 116, 48, 64, 79, 69, 73, 18, 45, 102, 133, 60, 207, 32, 117, 164
Offset: 1

Views

Author

Michel Marcus, Nov 23 2015

Keywords

Comments

Is this a permutation of the positive integers?

Examples

			The first 6 terms of A246946 are 6, 12, 18, 24, 30 and 10, that is, the 1st, 3rd, 6th, 10th, 13th and 2nd terms of A024619.

Links

Crossrefs

Cf. A024619, A246946.

Programs

  • Maple
    N:= 2000: # get all terms before the first term > N.
W:= Vector(N,t -> if nops(numtheory:-factorset(t))<=1 then 0 else 1 fi):
WS:= ListTools:-PartialSums(convert(W,list)):
m:= 1:
F:= {2,3}:
A[1]:= WS[6]:
W[6]:= 0:
for n from 2 do
  while W[m] = 0 and m < N do m:= m+1 od;
  for k from m to N do
     if W[k] = 1 and nops(numtheory:-factorset(k) intersect F) = 2 then
        A[n]:= WS[k];
        W[k]:= 0;
        F:= numtheory:-factorset(k);
        break
     fi
  od;
  if k > N then break fi;
od:
seq(A[i],i=1..n-1); # Robert Israel, Nov 23 2015
  • PARI
    v246946(nn) = {a = 6; fa = (factor(a)[,1])~; va = [a]; vs = va; k = 0; while (k!= nn, k = 1; while (!((#setintersect(fa, (factor(k)[,1])~) == 2) && (! vecsearch(vs, k))), k++); a = k; fa = (factor(a)[,1])~; va = concat(va, k); vs = vecsort(va);); va;}
v024619(nn) = {va = []; for (n=1, nn, if (omega(n) >= 2, va = concat(va, n));); va;}
lista(nn) = {v = v246946(nn); w = v024619(vecmax(v)); for (k=1, #v, for (j=1, #w, if (w[j] == v[k], print1(j, ", "); break);););}

A246947 a(1)=30; for n > 1, a(n) is the least integer not occurring earlier such that a(n) shares exactly three distinct prime divisors with a(n-1).

Original entry on oeis.org

30, 60, 90, 120, 150, 180, 210, 42, 84, 126, 168, 252, 294, 336, 378, 420, 70, 140, 280, 350, 490, 560, 630, 105, 315, 525, 735, 840, 240, 270, 300, 330, 66, 132, 198, 264, 396, 462, 154, 308, 616, 770, 110, 220, 440, 550, 660, 165, 495, 825, 990, 360, 390, 78
Offset: 1

Views

Author

Michel Lagneau, Sep 08 2014

Keywords

Comments

All terms belong to A000977. Is this a permutation of A000977? - Michel Marcus, Nov 24 2015

Examples

			90 is in the sequence because the common prime distinct divisors between a(2)=60 and a(3)=90 are 2, 3 and 5.

Links

Crossrefs

Cf. A000977, A064413, A246946.

Programs

  • Maple
    with(numtheory):a0:={2,3,5}:lst:={}:
for n from 1 to 100 do:
  ii:=0:
    for k from 30 to 50000 while(ii=0) do:
      y:=factorset(k):n0:=nops(y):lst1:={}:
        for j from 1 to n0 do:
        lst1:=lst1 union {y[j]}:
        od:
         a1:=a0 intersect lst1:
         if {k} intersect lst ={} and a1 <> {} and nops(a1)=3
          then
          printf(`%d, `,k):lst:=lst union {k}:a0:=lst1:ii:=1:
         else
         fi:
      od:
  od:
  • Mathematica
    f[s_List]:=Block[{m=s[[-1]],k=30},While[MemberQ[s,k]||Intersection[Transpose[FactorInteger[k]][[1]],Transpose[FactorInteger[m]][[1]]]=={}|| Length[Intersection[Transpose[FactorInteger[k]][[1]],Transpose[FactorInteger[m]][[1]]]]!=3,k++];Append[s,k]];Nest[f,{30},70]
  • PARI
    lista(nn) = {a = 30; print1(a, ", "); fa = (factor(a)[,1])~; va = [a]; k = 0; while (k!= nn, k = 1; while (!((#setintersect(fa, (factor(k)[,1])~) == 3) && (! vecsearch(va, k))), k++); a = k; print1(a, ", "); fa = (factor(a)[,1])~; va = vecsort(concat(va, k)););} \\ Michel Marcus, Nov 24 2015

A264664 a(1)=210; for n > 1, a(n) is the least integer not occurring earlier such that a(n) shares exactly four distinct prime divisors with a(n-1).

Original entry on oeis.org

210, 420, 630, 840, 1050, 1260, 1470, 1680, 1890, 2100, 2310, 330, 660, 990, 1320, 1650, 1980, 2640, 2970, 3300, 3630, 3960, 4290, 390, 780, 1170, 1560, 1950, 2340, 2730, 546, 1092, 1638, 2184, 3276, 3822, 4368, 4914, 5460, 910, 1820, 3640, 4550, 6370, 7280
Offset: 1

Views

Author

Michel Lagneau, Nov 20 2015

Keywords

Comments

The first odd term is a(47) = 1365. - Michel Marcus, Nov 21 2015

Examples

			630 is in the sequence because the common prime distinct divisors between a(2)=420 and a(3)=630 are 2, 3, 5 and 7.

Links

Crossrefs

Cf. A246946, A246947.

Programs

  • Maple
    with(numtheory):a0:={2, 3, 5, 7}:lst:={}:
for n from 1 to 100 do:
  ii:=0:
    for k from 210 to 50000 while(ii=0) do:
      y:=factorset(k):n0:=nops(y):lst1:={}:
        for j from 1 to n0 do:
        lst1:=lst1 union {y[j]}:
        od:
         a1:=a0 intersect lst1:
         if {k} intersect lst ={} and a1 <> {} and nops(a1)=4
          then
          printf(`%d, `, k):lst:=lst union {k}:a0:=lst1:ii:=1:
         else
         fi:
      od:
  od:
  • Mathematica
    a = {210}; Do[k = 1; While[Nand[! MemberQ[a, k], Length@ Intersection[First /@ FactorInteger@ a[[n - 1]], First /@ FactorInteger@ k] == 4], k++]; AppendTo[a, k], {n, 2, 45}]; a (* Michael De Vlieger, Nov 21 2015 *)

A264718 a(1)=2310; for n > 1, a(n) is the least integer not occurring earlier such that a(n) shares exactly five distinct prime divisors with a(n-1).

Original entry on oeis.org

2310, 4620, 6930, 9240, 11550, 13860, 16170, 18480, 20790, 23100, 25410, 27720, 30030, 2730, 5460, 8190, 10920, 13650, 16380, 19110, 21840, 24570, 27300, 32760, 35490, 38220, 40950, 43680, 46410, 3570, 7140, 10710, 14280, 17850, 21420, 24990, 28560, 32130
Offset: 1

Views

Author

Michel Lagneau, Nov 21 2015

Keywords

Comments

The first term a(1) = 2*3*5*7*11.

Examples

			46410 is in the sequence because the distinct prime divisors common to a(29) = 46410 = 2*3*5*7*13*17 and a(28) = 43680 = 2^5*3*5*7*13 are 2, 3, 5, 7 and 13.

Links

Crossrefs

Cf. A246946, A246947, A264664.

Programs

  • Maple
    with(numtheory):a0:={2, 3, 5, 7, 11}:lst:={}:
for n from 1 to 100 do:
  ii:=0:
    for k from 2310 to 50000 while(ii=0) do:
      y:=factorset(k):n0:=nops(y):lst1:={}:
        for j from 1 to n0 do:
        lst1:=lst1 union {y[j]}:
        od:
         a1:=a0 intersect lst1:
         if {k} intersect lst ={} and a1 <> {} and nops(a1)=5
          then
          printf(`%d, `, k):lst:=lst union {k}:a0:=lst1:ii:=1:
         else
         fi:
      od:
  od:
  • Mathematica
    a = {2310}; Do[k = 1; While[Nand[! MemberQ[a, k], Length@ Intersection[First /@ FactorInteger@ a[[n - 1]], First /@ FactorInteger@ k] == 5], k++]; AppendTo[a, k], {n, 2, 38}]; a (* Michael De Vlieger, Nov 21 2015 *)
Showing 1-4 of 4 results.

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