A317388 - OEIS

%I #8 Nov 20 2018 05:21:07

%S 39,24,25,26,28,30,31,34,35,37,39,41,43,44,46,48,49,51,52,53,54,56,57,

%T 58,60,61,62,63,65,66,68,69,70,72,73,74,76,77,79,80,81,83,84,85,86,87,

%U 88,89,90,92,93,94,95,96,98,99,100,101,102,103,105,106,107,108

%N a(n) is the smallest number having at least n partitions into n parts with the same product.

%H Byungchul Cha et al., <a href="https://arxiv.org/abs/1811.07451">An Investigation on Partitions with Equal Products</a>, arXiv:1811.07451 [math.NT], 2018.

%e a(4) = 24 because 24 is the smallest number which admits 4 partitions in 4 parts with the same product:

%e 24  = 12+5+4+3 = 10+8+3+3 = 10+6+6+2 = 9+8+5+2, and

%e 720 = 12*5*4*3 = 10*8*3*3 = 10*6*6*2 = 9*8*5*2.

%t a[n_] := Block[{k=n}, While[Max[Last /@ Tally[Times @@@ IntegerPartitions[k, {n}]]] < n, k++]; k]; Array[a, 40, 3]

%Y Cf. A119028.

%K nonn

%O 3,1

%A _Giovanni Resta_, Jul 27 2018