

A317388


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


1



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
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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



