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Search: id:A037032
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| A037032 |
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Total number of prime parts in all partitions of n. |
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+0
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; listen)
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OFFSET
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1,3
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FORMULA
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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
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p(3) = 1+1+1, 1+2, 3 -> {2, 3} = 2
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MAPLE
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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
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Cf. A000041.
Sequence in context: A109853 A127977 A112997 this_sequence A165753 A090752 A051058
Adjacent sequences: A037029 A037030 A037031 this_sequence A037033 A037034 A037035
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KEYWORD
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nonn
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AUTHOR
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G. L. Honaker, Jr. (honak3r(AT)gmail.com)
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EXTENSIONS
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More terms from Naohiro Nomoto (n_nomoto(AT)yabumi.com), Apr 19 2002
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