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

1,1

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.

Links

Table of n, a(n) for n=1..46.

Wikipedia, Geometric mean

Example

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}

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.

Sequence in context: A115444 A119385 A330243 * A332952 A308099 A308252

Adjacent sequences: A326643 A326644 A326645 * A326647 A326648 A326649

Keyword

nonn

Author

Gus Wiseman, Jul 16 2019

Status

approved