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A381630 a(n) is the least k such that the sum of k and the k-th number with n prime factors (counted with multiplicity) has n prime factors (counted with multiplicity).

%I A381630 #39 Mar 21 2025 14:22:40
%S A381630 1,4,8,14,16,16,96,80,304,448,640,1984,544,2048,3584,20480,9216,49152,
%T A381630 65536,524288,1245184,3309568,204800,1179648,28311552,2426880,
%U A381630 29360128,6291456,27787264,125829120,67108864,327155712,1073741824
%N A381630 a(n) is the least k such that the sum of k and the k-th number with n prime factors (counted with multiplicity) has n prime factors (counted with multiplicity).
%e A381630 a(3) = 8 because the 8th number with 3 prime factors (the 8th triprime) is 42 = 2*3*7, 8 + 42 = 50 = 2 * 5^2 also has 3 prime factors, and 8 is the smallest number that works.
%p A381630 f:= proc(n) uses priqueue; local pq,k,t,i,q;
%p A381630     initialize(pq);
%p A381630     insert([-2^n,2$n],pq);
%p A381630     for k from 1 do
%p A381630        t:= extract(pq);
%p A381630        if numtheory:-bigomega(k-t[1])=n then return k fi;
%p A381630        q:= nextprime(t[-1]);
%p A381630        for i from 1 to n while t[-i] = t[-1] do
%p A381630          insert([t[1]*(q/t[-1])^i,op(t[2..n+1-i]),q$i],pq);
%p A381630        od
%p A381630     od
%p A381630 end proc:
%p A381630 map(f, [$1..30]); # _Robert Israel_, Mar 07 2025
%Y A381630 Cf. A001222, A064402, A100915.
%K A381630 nonn,more
%O A381630 1,2
%A A381630 _Robert Israel_, Mar 07 2025
%E A381630 a(32) from _Jinyuan Wang_, Mar 09 2025
%E A381630 a(33) from _Jinyuan Wang_, Mar 21 2025