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A037032
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Total number of prime parts in all partitions of n.
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7
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0, 1, 2, 4, 7, 13, 20, 32, 48, 73, 105, 153, 214, 302, 415, 569, 767, 1034, 1371, 1817, 2380, 3110, 4025, 5199, 6659, 8512, 10806, 13684, 17229, 21645, 27049, 33728, 41872, 51863, 63988, 78779, 96645, 118322, 144406, 175884, 213617, 258957
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| a(n) = Sum_{k=1..n} A001221(k)*A000041(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 22 2002
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EXAMPLE
| Contribution from Omar E. Pol, Nov 20 2011 (Start):
For n = 6 we have:
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. Number of
Partitions prime parts
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6 .......................... 0
3 + 3 ...................... 2
4 + 2 ...................... 1
2 + 2 + 2 .................. 3
5 + 1 ...................... 1
3 + 2 + 1 .................. 2
4 + 1 + 1 .................. 0
2 + 2 + 1 + 1 .............. 2
3 + 1 + 1 + 1 .............. 1
2 + 1 + 1 + 1 + 1 .......... 1
1 + 1 + 1 + 1 + 1 + 1 ...... 0
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Total ..................... 13
So a(6) = 13. (End)
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MAPLE
| with(combinat): a:=proc(n) local P, c, j, i: P:=partition(n): c:=0: for j from 1 to numbpart(n) do for i from 1 to nops(P[j]) do if isprime(P[j][i])=true then c:=c+1 else c:=c fi: od: od: c: end: seq(a(n), n=1..42); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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CROSSREFS
| Cf. A000041.
Sequence in context: A164901 A109853 A112997 * A165753 A205183 A090752
Adjacent sequences: A037029 A037030 A037031 * A037033 A037034 A037035
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KEYWORD
| nonn
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AUTHOR
| G. L. Honaker, Jr. (honak3r(AT)gmail.com)
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EXTENSIONS
| More terms from Naohiro Nomoto (n_nomoto(AT)yabumi.com), Apr 19 2002
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