Voozh

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

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OFFSET

0,2

COMMENTS

a(6) > 33000000 if it exists.

a(7) = 5195190.

LINKS

Table of n, a(n) for n=0..5.

EXAMPLE

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.

MAPLE

f:= proc(n) local P, S, p, i;

P:= numtheory:-factorset(n);

S:= mul(add(x^(p^i), i=1..floor(log[p](n))), 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); # corrected by Robert Israel, Feb 20 2026