A326646 Heinz numbers of non-constant integer partitions whose mean and geometric mean are both integers.

46, 57, 183, 194, 228, 371, 393, 454, 515, 687, 742, 838, 1057, 1064, 1077, 1150, 1157, 1159, 1244, 1322, 1563, 1895, 2018, 2060, 2116, 2157, 2163, 2167, 2177, 2225, 2231, 2405, 2489, 2854, 2859, 3249, 3263, 3339, 3352, 3558, 3669, 3758, 3787, 3914, 4265, 4351

Offset: 1

Author

Gus Wiseman, Jul 16 2019

Keywords

• nonn

Comments

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

The enumeration of these partitions by sum is given by A326642.

Examples

			The sequence of terms together with their prime indices begins:
    46: {1,9}
    57: {2,8}
   183: {2,18}
   194: {1,25}
   228: {1,1,2,8}
   371: {4,16}
   393: {2,32}
   454: {1,49}
   515: {3,27}
   687: {2,50}
   742: {1,4,16}
   838: {1,81}
  1057: {4,36}
  1064: {1,1,1,4,8}
  1077: {2,72}
  1150: {1,3,3,9}
  1157: {6,24}
  1159: {8,18}
  1244: {1,1,64}
  1322: {1,121}
		

Links

• Wikipedia, Geometric mean

Crossrefs

Heinz numbers of partitions with integer mean and geometric mean are A326645.

Heinz numbers of partitions with integer mean are A316413.

Heinz numbers of partitions with integer geometric mean are A326623.

Non-constant partitions with integer mean and geometric mean are A326642.

Subsets with integer mean and geometric mean are A326643.

Strict partitions with integer mean and geometric mean are A326029.

Cf. A051293, A067538, A067539, A078175, A082553, A102627, A326027, A326641, A326644, A326647.