A384842 a(n) is the n-th number which can be represented as the sum of n distinct n-almost primes in exactly n ways, or -1 if fewer than n such numbers exist.

2, 24, 75, 211, 522, 1332, 3588, 8900, 20552, 48304, 118768, 256864, 558272, 1564608, 2863360

Offset: 1

Author

Robert Israel, Jun 10 2025

Keywords

• nonn
• more

Examples

			For n = 2, the first number that is the sum of two distinct semiprimes in exactly two ways is A365494(2) = 19, and the second is a(2) = 24 = 9 + 15 = 10 + 14.
		

Crossrefs

Cf. A091538, A365494.

Programs

Maple

f:= proc(n) uses priqueue; local pq, S, t, x, y, k, i, p, v, R;
     initialize(pq);
     insert([-2^n, 2$n], pq);
     S[0]:= 1:
     for i from 1 to n do S[i]:= 0 od:
     do
       t:= extract(pq);
       x:= -t[1];
       for i from n to 1 by -1 do
         S[i]:= expand(S[i] + S[i-1] * y^x);
       od;
       if type(S[n], `+`) then
         R:= select(t -> degree(t, y) < x and eval(t, y=1) = n, convert(S[n], list));
         if nops(R) >= n then R:= sort(map(t -> degree(t,y), R)); return R[n] fi;
       fi;
       p:= nextprime(t[-1]);
       for i from n+1 to 2 by -1 while t[i] = t[-1] do
        v:= x*(p/t[-1])^(n+2-i);
        insert([-v, op(t[2..i-1]), p$(n+2-i)], pq)
       od;
     od;
end proc:
map(f, [$1..15]);