A214343 a(n) is the smallest integer j such that the numbers of prime factors (counting multiplicity) in j, j+1, ... , j+n-1 are the full set {1,2,...,n}.

2, 3, 6, 15, 77, 726, 6318, 189375, 755968, 871593371, 33714015615

Offset: 1

Author

Jake Foster, Jul 13 2012

Keywords

• nonn

Comments

Next term a(10) > 5*10^7. Joerg Arndt, Jul 14 2012

Examples

			a(4)=15 because 15 has two prime factors, 16 has four, 17 has one and 18 has three (and 15 is the smallest number with this property).
a(5) = 77 because 77, 78, 79, 80 and 81 have 2, 3, 1, 5 and 4 prime factors.
		

Crossrefs

Cf. A072875, A001222.

Programs

Maple

A214343 := proc(n)
    refs := {seq(i,i=1..n)} ;
    for j from 1 do
        pf := {} ;
        for k from 0 to n-1 do
            pf := pf union {numtheory[bigomega](j+k)} ;
            if nops(pf) < k+1 then
                break;
            end if;
        end do:
        if pf = refs then
            return j;
        end if;
    end do:
end proc: # R. J. Mathar, Jul 13 2012

Mathematica

f[n_] := f[n] = FactorInteger[n][[All, 2]] // Total;
n = 1;
i = 2;
While[True,
  While[Union[Table[f[j], {j, i, i + n - 1}]] != Range[n],
   i += 1; f[i] =.
   ];
  Print[i]; n += 1;
  ];

Extensions

a(10)-a(11) from Donovan Johnson, Jul 15 2012