|
|
A327473
|
|
Heinz numbers of integer partitions whose mean A326567/A326568 is a part.
|
|
67
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
|
|
LINKS
|
|
|
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
|
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.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|