A317388 a(n) is the smallest number having at least n partitions into n parts with the same product.

39, 24, 25, 26, 28, 30, 31, 34, 35, 37, 39, 41, 43, 44, 46, 48, 49, 51, 52, 53, 54, 56, 57, 58, 60, 61, 62, 63, 65, 66, 68, 69, 70, 72, 73, 74, 76, 77, 79, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 98, 99, 100, 101, 102, 103, 105, 106, 107, 108

Offset: 3

Author

Giovanni Resta, Jul 27 2018

Keywords

• nonn

Examples

			a(4) = 24 because 24 is the smallest number which admits 4 partitions in 4 parts with the same product:
24  = 12+5+4+3 = 10+8+3+3 = 10+6+6+2 = 9+8+5+2, and
720 = 12*5*4*3 = 10*8*3*3 = 10*6*6*2 = 9*8*5*2.
		

Links

• Byungchul Cha et al., An Investigation on Partitions with Equal Products, arXiv:1811.07451 [math.NT], 2018.

Crossrefs

Cf. A119028.

Programs

Mathematica

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