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).

1, 4, 6, 8, 8, 12, 12, 12, 15, 16, 16, 16, 18, 20, 24, 24, 24, 24, 24, 28, 27, 32, 30, 48, 32, 32, 32, 36, 36, 36, 42, 40, 40, 48, 48, 48, 45, 48, 48, 48, 48, 48, 54, 60, 54, 56, 54, 60, 63, 60, 60, 60, 63, 64, 64, 64, 64, 64, 70, 72, 72, 72, 72, 72, 72, 84, 80, 80, 81, 80, 80

Offset: 1

Author

Louis Marmet (louis(AT)marmet.org), Mar 10 2005

Keywords

• easy
• nonn

Examples

			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.
		

Links

• David Radcliffe, Table of n, a(n) for n = 1..10000
• Project Euler, Problem 88: Product-sum numbers

Programs

Mathematica

Table[k=1;While[Select[IntegerPartitions[k,{n}],Total@#==Times@@#&]=={},k++];k,{n,71}] (* Giorgos Kalogeropoulos, Dec 07 2021 *)

Formula

a(n) <= 2n, since 1^(n-2)*2*n = (n-2)*1 + 2 + n. - Étienne Dupuis, Dec 07 2021