cp's OEIS Frontend

A104173 a(n) is the smallest integer equal to the sum and the product of the same n positive integers: a(n) = i(1) + i(2) + ... + i(n) = i(1)*i(2)*...*i(n).

%I A104173 #23 Dec 19 2021 04:21:12
%S A104173 1,4,6,8,8,12,12,12,15,16,16,16,18,20,24,24,24,24,24,28,27,32,30,48,
%T A104173 32,32,32,36,36,36,42,40,40,48,48,48,45,48,48,48,48,48,54,60,54,56,54,
%U A104173 60,63,60,60,60,63,64,64,64,64,64,70,72,72,72,72,72,72,84,80,80,81,80,80
%N A104173 a(n) is the smallest integer equal to the sum and the product of the same n positive integers: a(n) = i(1) + i(2) + ... + i(n) = i(1)*i(2)*...*i(n).
%H A104173 David Radcliffe, <a href="/A104173/b104173.txt">Table of n, a(n) for n = 1..10000</a>
%H A104173 Project Euler, <a href="https://projecteuler.net/problem=88">Problem 88: Product-sum numbers</a>
%F A104173 a(n) <= 2n, since 1^(n-2)*2*n = (n-2)*1 + 2 + n. - _Étienne Dupuis_, Dec 07 2021
%e A104173 a(6)=12 because 6+2+1+1+1+1 = 6*2*1*1*1*1 = 12 is the smallest integer which is the sum and product of the same 6 positive integers.
%t A104173 Table[k=1;While[Select[IntegerPartitions[k,{n}],Total@#==Times@@#&]=={},k++];k,{n,71}] (* _Giorgos Kalogeropoulos_, Dec 07 2021 *)
%K A104173 easy,nonn
%O A104173 1,2
%A A104173 Louis Marmet (louis(AT)marmet.org), Mar 10 2005