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

3,1

Links

Table of n, a(n) for n=3..66.

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

Example

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.

Mathematica

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

Crossrefs

Cf. A119028.

Sequence in context: A033359 A326791 A268854 * A088344 A268856 A273597

Adjacent sequences: A317385 A317386 A317387 * A317389 A317390 A317391

Keyword

nonn

Author

Giovanni Resta, Jul 27 2018

Status

approved