OFFSET
3,1
LINKS
Byungchul Cha et al., An Investigation on Partitions with Equal Products, arXiv:1811.07451 [math.NT], 2018.
John B. Kelly, Partitions with equal products, Proc. Amer. Math. Soc. 15 (1964), 987-990.
EXAMPLE
a(3)=19. From s=19 onward, there are at least 2 different partitions of s into 3 parts with equal products:
s=19: {12,4,3} & {9,8,2}:
12 + 4 + 3 = 9 + 8 + 2 = 19;
12 * 4 * 3 = 9 * 8 * 2 = 144;
s=20: {15,3,2} & {10,9,1}:
15 + 3 + 2 = 10 + 9 + 1 = 20;
15 * 3 * 2 = 10 * 9 * 1 = 90;
s=21: {16,3,2} & {12,8,1}:
16 + 3 + 2 = 12 + 8 + 1 = 21;
16 * 3 * 2 = 12 * 8 * 1 = 96.
MATHEMATICA
Do[maxsumnotwork = 0; Do[intpart = IntegerPartitions[sum, {n}]; prod = Table[Times @@ intpart[[i]], {i, Length[intpart]}]; prodtally = Tally[prod]; repeatprod = Select[prodtally, #[[2]] >= n - 1 &]; If[repeatprod == {}, maxsumnotwork = sum], {sum, 12, 200}]; Print[n, " ", maxsumnotwork + 1], {n, 3, 60}]
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
STATUS
approved