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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
Sequence in context: A174184 A278485 A279064 * A294263 A345745 A280110
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 22 2017
STATUS
approved

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Last modified July 19 20:58 EDT 2024. Contains 374436 sequences. (Running on oeis4.)