|
| |
|
|
A301900
|
|
Heinz numbers of strict non-knapsack partitions. Squarefree numbers such that more than one divisor has the same Heinz weight A056239(d).
|
|
13
|
|
|
|
30, 70, 154, 165, 210, 273, 286, 330, 390, 442, 462, 510, 546, 561, 570, 595, 646, 690, 714, 741, 770, 858, 870, 874, 910, 930, 1045, 1110, 1122, 1155, 1173, 1190, 1230, 1254, 1290, 1326, 1330, 1334, 1365, 1410, 1430, 1482, 1495, 1590, 1610, 1653, 1770
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
An integer partition is knapsack if every distinct submultiset has a different sum. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
|
|
|
LINKS
|
|
|
|
FORMULA
|
|
|
|
EXAMPLE
|
Sequence of strict non-knapsack partitions begins: (321), (431), (541), (532), (4321), (642), (651), (5321), (6321), (761), (5421), (7321), (6421), (752), (8321), (743), (871), (9321), (7421), (862), (5431), (6521).
|
|
|
MATHEMATICA
|
wt[n_]:=If[n===1, 0, Total[Cases[FactorInteger[n], {p_, k_}:>k*PrimePi[p]]]];
Select[Range[1000], SquareFreeQ[#]&&!UnsameQ@@wt/@Divisors[#]&]
|
|
|
CROSSREFS
|
Cf. A000712, A005117, A056239, A108917, A112798, A122768, A275972, A276024, A284640, A296150, A299701, A299702, A299729, A301829, A301854, A301899.
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
