|
|
A325763
|
|
Heinz numbers of integer partitions whose consecutive subsequence-sums cover an initial interval of positive integers.
|
|
6
|
|
|
1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 32, 36, 40, 48, 54, 56, 60, 64, 72, 80, 96, 100, 108, 112, 120, 128, 144, 160, 162, 168, 176, 180, 192, 200, 216, 224, 240, 256, 280, 288, 300, 320, 324, 336, 352, 360, 384, 392, 400, 416, 432, 448, 480, 486, 500, 504, 512
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
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 appears to be A002865.
|
|
LINKS
|
|
|
EXAMPLE
|
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
4: {1,1}
6: {1,2}
8: {1,1,1}
12: {1,1,2}
16: {1,1,1,1}
18: {1,2,2}
20: {1,1,3}
24: {1,1,1,2}
32: {1,1,1,1,1}
36: {1,1,2,2}
40: {1,1,1,3}
48: {1,1,1,1,2}
54: {1,2,2,2}
56: {1,1,1,4}
60: {1,1,2,3}
64: {1,1,1,1,1,1}
72: {1,1,1,2,2}
80: {1,1,1,1,3}
|
|
MATHEMATICA
|
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Range[Total[primeMS[#]]]==Union[ReplaceList[primeMS[#], {___, s__, ___}:>Plus[s]]]&]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|