|
|
A325991
|
|
Heinz numbers of integer partitions such that not every orderless pair of distinct parts has a different sum.
|
|
7
|
|
|
210, 420, 462, 630, 840, 858, 910, 924, 1050, 1155, 1260, 1326, 1386, 1470, 1680, 1716, 1820, 1848, 1870, 1890, 1938, 2100, 2145, 2310, 2470, 2520, 2574, 2622, 2652, 2730, 2772, 2926, 2940, 3150, 3234, 3315, 3360, 3432, 3465, 3570, 3640, 3696, 3740, 3780, 3876
(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:
210: {1,2,3,4}
420: {1,1,2,3,4}
462: {1,2,4,5}
630: {1,2,2,3,4}
840: {1,1,1,2,3,4}
858: {1,2,5,6}
910: {1,3,4,6}
924: {1,1,2,4,5}
1050: {1,2,3,3,4}
1155: {2,3,4,5}
1260: {1,1,2,2,3,4}
1326: {1,2,6,7}
1386: {1,2,2,4,5}
1470: {1,2,3,4,4}
1680: {1,1,1,1,2,3,4}
1716: {1,1,2,5,6}
1820: {1,1,3,4,6}
1848: {1,1,1,2,4,5}
1870: {1,3,5,7}
1890: {1,2,2,2,3,4}
|
|
MATHEMATICA
|
Select[Range[1000], !UnsameQ@@Plus@@@Subsets[PrimePi/@First/@FactorInteger[#], {2}]&]
|
|
CROSSREFS
|
The integer partition case is A325857.
The strict integer partition case is A325877.
Heinz numbers of the counterexamples are given by A325991.
Cf. A002033, A056239, A103300, A108917, A112798, A143823, A196724, A325853, A325855, A325858, A325859, A325862, A325992, A325993, A325994.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|