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A334260
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Sum of the largest composite parts in the partitions of 2n into two parts.
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0
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0, 0, 4, 10, 23, 33, 39, 68, 76, 85, 116, 138, 175, 228, 242, 257, 306, 375, 393, 470, 490, 511, 578, 624, 697, 773, 799, 881, 966, 1024, 1054, 1179, 1276, 1309, 1412, 1447, 1483, 1632, 1747, 1786, 1907, 1989, 2116, 2289, 2333, 2469, 2608, 2797, 2845, 2993, 3043
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OFFSET
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1,3
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LINKS
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Table of n, a(n) for n=1..51.
Index entries for sequences related to partitions
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FORMULA
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a(n) = Sum_{i=1..n} (2*n-i) * (1 - c(2*n-i)) * (1 - [2*n-i = 1]), where [] is the Iverson bracket and c is the prime characteristic (A010051).
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EXAMPLE
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a(5) = 23; 2*5 = 10 has 3 partitions into two parts with largest part composite, (9,1), (8,2) and (6,4). The sum is then 9 + 8 + 6 = 23.
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MATHEMATICA
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Table[Sum[(2 n - i) (1 - PrimePi[2 n - i] + PrimePi[2 n - i - 1]) (1 - KroneckerDelta[2 n - i, 1]), {i, n}], {n, 80}]
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CROSSREFS
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Cf. A010051.
Sequence in context: A241430 A023378 A276308 * A038423 A002071 A024980
Adjacent sequences: A334257 A334258 A334259 * A334261 A334262 A334263
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KEYWORD
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nonn,easy
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AUTHOR
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Wesley Ivan Hurt, Apr 20 2020
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STATUS
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approved
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