A368498 - OEIS

%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