A327473 Heinz numbers of integer partitions whose mean A326567/A326568 is a part.

2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 30, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 84, 89, 90, 97, 101, 103, 105, 107, 109, 110, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..61.

Example

The sequence of terms together with their prime indices begins:
   2: {1}
   3: {2}
   4: {1,1}
   5: {3}
   7: {4}
   8: {1,1,1}
   9: {2,2}
  11: {5}
  13: {6}
  16: {1,1,1,1}
  17: {7}
  19: {8}
  23: {9}
  25: {3,3}
  27: {2,2,2}
  29: {10}
  30: {1,2,3}
  31: {11}
  32: {1,1,1,1,1}
  37: {12}

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], MemberQ[primeMS[#], Mean[primeMS[#]]]&]

Crossrefs

A subsequence of A316413.

Complement of A327476.

The enumeration of these partitions by sum is given by A237984.

Subsets whose mean is a part are A065795.

Numbers whose binary indices include their mean are A327478.

Cf. A000016, A056239, A067538, A112798, A240850, A325706, A326567/A326568.

Sequence in context: A089352 A086486 A071139 * A326837 A326847 A298538

Adjacent sequences: A327470 A327471 A327472 * A327474 A327475 A327476

Keyword

nonn

Author

Gus Wiseman, Sep 13 2019

Status

approved