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
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
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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);
Comments