A368498 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.

1, 2, 30, 270, 2730, 4290

Offset: 0

Author

Robert Israel, Dec 27 2023

Keywords

• nonn
• more

Comments

a(6) > 33000000 if it exists.

a(7) = 5195190.

Examples

			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.
		

Crossrefs

Cf. A366914.

Programs

Maple

f:= proc(n) local P,S,p,i;
  P:= numtheory:-factorset(n);
  S:= mul(add(x^(p^i),i=1..floor(log[p](n0)),p=P);
coeff(S,x,n);
end proc:
V:= Array(0..4): count:= 0:
for n from 1 while count < 5 do
v:= f(n):
  if V[v] = 0 then V[v]:= n; count:= count+1 fi;
od:
convert(V,list);