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A096223
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Let p(k) be the number of partitions of k (A000041); a(n) = sum{1<=k<=n, GCD(k,n)=1} p(k).
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0
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1, 1, 3, 4, 11, 8, 29, 26, 52, 49, 138, 79, 271, 198, 337, 389, 914, 477, 1596, 993, 1881, 1912, 4507, 2222, 6485, 5080, 8682, 7384, 18459, 6780, 28628, 19598, 31098, 29444, 53198, 30470, 99132, 65771, 104464, 80422, 215307, 81792, 313064, 195091, 272503
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| If we let mu() be the Moebius function (A008683), then a(n) = sum mu(j), where j is taken over all parts, with repetitions, of every partition of n and where each j is such that j|n. Example: The 7 partitions of 5 are: 1+1+1+1+1, 1+1+1+2, 1+1+3, 1+2+2, 2+3, 1+4, 5. Of these parts, only 1 and 5 divide 5. Since there are twelve 1's and one 5, we have a(5) = 12*mu(1) + 1*mu(5) = 11.
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MATHEMATICA
| f[n_] := Block[{s = 0, k = 1}, While[k < n + 1, If[ GCD[k, n] == 1, s = s + PartitionsP[k]]; k++ ]; s]; Table[ f[n], {n, 45}] (from Robert G. Wilson v Jul 29 2004)
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CROSSREFS
| Cf. A008683.
Sequence in context: A198299 A175317 A056045 * A195589 A047457 A098377
Adjacent sequences: A096220 A096221 A096222 * A096224 A096225 A096226
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KEYWORD
| nonn,easy
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AUTHOR
| Leroy Quet Jul 29 2004
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EXTENSIONS
| Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 29 2004
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