%I #17 Dec 31 2023 10:23:45
%S 1,2,30,270,2730,4290
%N a(n) is the smallest number that can be written in exactly n ways as the sum of positive integer powers of its distinct prime factors, or -1 if no such number exists.
%C a(6) > 33000000 if it exists.
%C a(7) = 5195190.
%e a(3) = 270 because the distinct prime factors of 270 are 2, 3, 5, and 270 = 2^1 + 3^5 + 5^2 = 2^6 + 3^4 + 5^3 = 2^8 + 3^2 + 5^1 can be written in exactly 3 ways as the sum of positive integer powers of 2, 3 and 5.
%p f:= proc(n) local P,S,p,i;
%p P:= numtheory:-factorset(n);
%p S:= mul(add(x^(p^i),i=1..floor(log[p](n0)),p=P);
%p coeff(S,x,n);
%p end proc:
%p V:= Array(0..4): count:= 0:
%p for n from 1 while count < 5 do
%p v:= f(n):
%p if V[v] = 0 then V[v]:= n; count:= count+1 fi;
%p od:
%p convert(V,list);
%Y Cf. A366914.
%K nonn,more
%O 0,2
%A _Robert Israel_, Dec 27 2023