|
|
A325457
|
|
Heinz numbers of integer partitions with strictly decreasing differences.
|
|
10
|
|
|
1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 25, 26, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 49, 50, 51, 53, 55, 57, 58, 59, 61, 62, 65, 67, 69, 70, 71, 73, 74, 75, 77, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 98
(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 differences of a sequence are defined as if the sequence were increasing, so for example the differences of (6,3,1) are (-3,-2).
The enumeration of these partitions by sum is given by A320470.
|
|
LINKS
|
|
|
EXAMPLE
|
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
3: {2}
4: {1,1}
5: {3}
6: {1,2}
7: {4}
9: {2,2}
10: {1,3}
11: {5}
12: {1,1,2}
13: {6}
14: {1,4}
15: {2,3}
17: {7}
19: {8}
20: {1,1,3}
21: {2,4}
22: {1,5}
23: {9}
|
|
MATHEMATICA
|
primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]];
Select[Range[100], Greater@@Differences[primeptn[#]]&]
|
|
CROSSREFS
|
Cf. A056239, A112798, A320470, A320510, A325328, A325352, A325360, A325361, A325368, A325399, A325456, A325461, A320470, A325396.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|