A374816 - OEIS

%I #17 Aug 06 2024 09:55:26

%S 0,2,6,116,350,14130,6626906,998632866,150811201250

%N a(n) is the least k > a(n-1) such that k - a(i) for i = 0 .. n-1 all have exactly n prime factors, counted with multiplicity; a(0) = 0.

%C A008776(n) and A008776(n) - A008776(n-1) have n prime factors, counted with multiplicity, and it appears that A008776(n) is the least k with this property.

%e a(1) = 2 is prime.

%e a(2) = 6 = 2 * 3 and 6 - 2 = 4 = 2^2 have 2 prime factors, counted with multiplicity.

%e a(3) = 116 = 2^2 * 29, 116 - 2 = 114 = 2 * 3 * 19 and 116 - 6 = 110 = 2 * 5 * 11 have 3 prime factors, counted with multiplicity.

%p A[0]:= 0:

%p for i from 1 to 6 do

%p   for x from A[i-1]+1 do

%p     if andmap(t -> numtheory:-bigomega(x-t)=i,[seq(A[j],j=0..i-1)]) then

%p       A[i]:= x;

%p       break

%p     fi

%p od od:

%p seq(A[i],i=0..6);

%Y Cf. A001222, A008776, A361228.

%K nonn,more

%O 0,2

%A _Zak Seidov_ and _Robert Israel_, Jul 20 2024

%E a(8) from _Daniel Suteu_, Aug 06 2024