A326625 Number of strict integer partitions of n whose geometric mean is an integer.

0, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 1, 1, 3, 2, 2, 1, 2, 1, 2, 4, 3, 1, 2, 1, 4, 5, 2, 3, 3, 3, 5, 1, 3, 5, 5, 3, 4, 4, 7, 7, 5, 5, 2, 4, 2, 5, 7, 4, 6, 9, 5, 7, 7, 8, 7, 5, 11, 5, 9, 9, 9, 7, 9, 5, 13, 7, 9, 7, 11, 12, 7, 7, 12, 9, 13, 11, 10, 13, 7, 14

Offset: 0

Author

Gus Wiseman, Jul 14 2019

Keywords

• nonn

Examples

			The a(63) = 9 partitions:
  (63)  (36,18,9)  (54,4,3,2)   (36,18,6,2,1)   (36,9,8,6,3,1)
        (48,12,3)  (27,24,8,4)  (18,16,12,9,8)
                   (32,18,9,4)
The initial terms count the following partitions:
   1: (1)
   2: (2)
   3: (3)
   4: (4)
   5: (5)
   5: (4,1)
   6: (6)
   7: (7)
   7: (4,2,1)
   8: (8)
   9: (9)
  10: (10)
  10: (9,1)
  10: (8,2)
  11: (11)
  12: (12)
  13: (13)
  13: (9,4)
  13: (9,3,1)
  14: (14)
  14: (8,4,2)
  15: (15)
  15: (12,3)
  16: (16)
		

Links

• Wikipedia, Geometric mean

Crossrefs

Partitions whose geometric mean is an integer are A067539.

Strict partitions whose average is an integer are A102627.

Cf. A078174, A078175, A326027, A326567/A326568, A326623, A326624.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&IntegerQ[GeometricMean[#]]&]],{n,0,30}]