A364266
The first term in a chain of at least 3 consecutive numbers each with exactly 5 distinct prime factors.
Original entry on oeis.org
1042404, 3460280, 3818828, 3998664, 4638984, 4991964, 5540248, 5701254, 5715500, 5964958, 6772050, 6794084, 7237384, 7453964, 7459088, 7745318, 7757034, 7993194, 8083634, 8153430, 8168194, 8273628, 8340834, 8340980, 8414756, 8486994, 8698898, 8722634, 8758904
Offset: 1
1042404 = 2^2*3*11*53*149, 1042405 = 5*6*143*29*79 and 1042406 = 2*17*23*31*43 each have 5 distinct prime factors, so 1042404 is in the sequence.
-
omega := proc(n)
nops(numtheory[factorset](n)) ;
end proc:
for k from 1 do
if omega(k) = 5 then
if omega(k+1) = 5 then
if omega(k+2) = 5 then
print(k) ;
end if;
end if;
end if;
end do:
-
seq[lim_] := Module[{s = {}, q1 = False, q2 = False, q3}, Do[q3 = PrimeNu[k] == 5; If[q1 && q2 && q3, AppendTo[s, k-2]]; q1 = q2; q2 = q3, {k, 3, lim}]; s]; seq[10^7] (* Amiram Eldar, Oct 01 2024 *)
A087977
a(n) is the first term in the first chain of at least n consecutive numbers each having exactly four distinct prime factors.
Original entry on oeis.org
210, 7314, 37960, 134043, 357642, 1217250, 1217250, 14273478, 44939642, 76067298, 163459742, 547163235, 2081479430, 2771263512, 11715712410, 17911205580, 56608713884, 118968284928, 118968284928, 585927201062, 585927201062, 585927201062, 585927201062
Offset: 1
a(6) = a(7) = 1217250 because the relevant 7 successive numbers have 4 distinct prime factors:
1217250 = 2 * 3^2 * 5^3 * 541;
1217251 = 7 * 17 * 53 * 193;
1217252 = 2^2 * 23 * 101 * 131;
1217253 = 3 * 47 * 89 * 97;
1217254 = 2 * 19 * 103 * 311;
1217255 = 5 * 13 * 61 * 307;
1217256 = 2^3 * 3 * 67 * 757.
-
k=1; Do[While[Union[Table[Length[FactorInteger[i]], {i, k, k+n-1}]]!={4}, k++ ]; Print[k], {n, 1, 8}]
Module[{d4=Table[If[PrimeNu[n]==4,1,0],{n,143*10^5}]},Flatten[Table[ SequencePosition[d4,PadRight[{},n,1],1],{n,8}],1][[All,1]]] (* Requires Mathematica version 10 or later *) (* This generates the first 8 terms of the sequence *) (* Harvey P. Dale, Aug 25 2017 *)
A138206
a(n) is the first term in a chain of at least n consecutive numbers each with exactly 6 distinct prime factors.
Original entry on oeis.org
30030, 11243154, 323567034, 7933641735, 45212320502, 626804494291, 7563009743844, 83793300096830, 395732828592408
Offset: 1
A138207
a(n) is the first term in a chain of at least n consecutive numbers each with exactly 7 distinct prime factors.
Original entry on oeis.org
510510, 965009045, 30989984674, 1673602584618, 66298619667606
Offset: 1
A154573
a(n) is the first term in a chain of at least n consecutive numbers each with exactly 8 distinct prime factors.
Original entry on oeis.org
9699690, 65893166030, 10042712381260, 1126299564879684
Offset: 1
A384507
Initial term of first run of exactly n consecutive numbers with exactly 5 distinct prime factors.
Original entry on oeis.org
2310, 254540, 1042404, 21871365, 129963314, 830692265, 4617927894, 18297409143, 41268813542, 287980277114, 1182325618032, 6455097761454, 14207465691240, 54049709480208, 90987640183352, 1164838922284960, 546525829796442
Offset: 1
a(16) > a(17) because the first run of 16 consecutive integers i with A001221(i)=5 is not a maximal run.
Showing 1-6 of 6 results.
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