

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).


5



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
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OFFSET

1,2


LINKS



FORMULA

a(n) <= 2n, since 1^(n2)*2*n = (n2)*1 + 2 + n.  Étienne Dupuis, Dec 07 2021


EXAMPLE

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.


MATHEMATICA

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


CROSSREFS



KEYWORD

easy,nonn


AUTHOR

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


STATUS

approved



