|
|
A294109
|
|
Sum of the larger parts of the partitions of n into two parts with smaller part prime.
|
|
1
|
|
|
0, 0, 0, 2, 3, 7, 9, 11, 13, 20, 23, 26, 29, 39, 43, 47, 51, 55, 59, 63, 67, 82, 87, 92, 97, 115, 121, 127, 133, 139, 145, 151, 157, 180, 187, 194, 201, 227, 235, 243, 251, 259, 267, 275, 283, 314, 323, 332, 341, 350, 359, 368, 377, 386, 395, 404, 413, 451
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{i=1..floor(n/2)} (n - i) * c(i), where c is the prime characteristic (A010051).
|
|
MATHEMATICA
|
Table[Sum[(n - i) (PrimePi[i] - PrimePi[i - 1]), {i, Floor[n/2]}], {n, 80}]
Table[Total[Select[IntegerPartitions[n, {2}], PrimeQ[#[[2]]]&][[All, 1]]], {n, 80}] (* Harvey P. Dale, Jul 08 2019 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|