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A326957
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Total number of noncomposite parts in all partitions of n.
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2
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0, 1, 3, 6, 11, 19, 32, 50, 77, 115, 170, 244, 348, 486, 675, 923, 1253, 1682, 2246, 2968, 3904, 5094, 6616, 8533, 10962, 13997, 17808, 22538, 28426, 35689, 44670, 55678, 69199, 85692, 105826, 130261, 159935, 195778, 239092, 291191, 353854, 428925, 518848
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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For n = 6 we have:
--------------------------------------
. Number of
Partitions noncomposite
of 6 parts
--------------------------------------
6 .......................... 0
3 + 3 ...................... 2
4 + 2 ...................... 1
2 + 2 + 2 .................. 3
5 + 1 ...................... 2
3 + 2 + 1 .................. 3
4 + 1 + 1 .................. 2
2 + 2 + 1 + 1 .............. 4
3 + 1 + 1 + 1 .............. 4
2 + 1 + 1 + 1 + 1 .......... 5
1 + 1 + 1 + 1 + 1 + 1 ...... 6
------------------------------------
Total ..................... 32
So a(6) = 32.
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0 or i=1, [1, n], b(n, i-1)+
(p-> p+[0, `if`(isprime(i), p[1], 0)])(b(n-i, min(n-i, i))))
end:
a:= n-> b(n$2)[2]:
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MATHEMATICA
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b[n_] := Sum[PrimeNu[k] PartitionsP[n-k], {k, 1, n}];
c[n_] := SeriesCoefficient[Product[1/(1-x^k), {k, 1, n}]/(1-x), {x, 0, n}];
a[n_] := b[n] + c[n-1];
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CROSSREFS
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First differs from A183088 at a(13).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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