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A294487 Sum of the lengths of the distinct rectangles with prime length and integer width such that L + W = n, W < L. 1
0, 0, 2, 3, 3, 5, 5, 12, 12, 7, 7, 18, 18, 24, 24, 24, 24, 41, 41, 60, 60, 49, 49, 72, 72, 59, 59, 59, 59, 88, 88, 119, 119, 102, 102, 102, 102, 120, 120, 120, 120, 161, 161, 204, 204, 181, 181, 228, 228, 228, 228, 228, 228, 281, 281, 281, 281, 252, 252, 311 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Sum of the largest parts of the partitions of n into two distinct parts with largest part prime.
LINKS
FORMULA
a(n) = Sum_{i=1..floor((n-1)/2)} (n-i) * A010051(n-i).
a(n) = n*A294602(n) - A368058(n). - Wesley Ivan Hurt, Dec 09 2023
EXAMPLE
a(14) = 24; the rectangles are 1 X 13 and 3 X 11 (7 X 7 is not considered since W < L). The sum of the lengths is then 13 + 11 = 24.
MATHEMATICA
Table[ Sum[(n - i)*(PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[(n-1)/2]}], {n, 60}]
PROG
(PARI) a(n) = sum(i=1, (n-1)\2, (n-i)*isprime(n-i)); \\ Michel Marcus, Nov 08 2017
CROSSREFS
Sequence in context: A051032 A106530 A273156 * A212792 A281363 A050976
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 31 2017
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)