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Search: id:A085410
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| A085410 |
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Total number of parts in all partitions of n into relatively prime parts. |
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+0
1
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| 1, 2, 5, 9, 19, 27, 53, 74, 122, 170, 274, 355, 555, 724, 1043, 1377, 1964, 2487, 3497, 4429, 5993, 7622, 10205, 12701, 16831, 20964, 27166, 33756, 43452, 53296, 68134, 83464, 105086, 128495, 160803, 195006, 242811, 293701, 362026, 436842, 536103
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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Moebius transform of A006128: Sum_{d|n} mu(n/d)*A006128(d).
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EXAMPLE
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Partitions of 6 into relatively prime parts are: 1+1+1+1+1+1, 1+1+1+1+2, 1+1+2+2, 1+1+1+3, 1+2+3, 1+1+4, 1+5; total number of parts is a(6)=6+5+4+4+3+3+2=27.
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MATHEMATICA
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f[n_] := Sum[DivisorSigma[0, m] PartitionsP[n - m], {m, 1, n}]; MT[n_] := Block[{d = Divisors[n]}, Plus @@ (MoebiusMu /@ (n/d)*f /@ d)]; Table[ MT[n], {n, 1, 41}]
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CROSSREFS
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Cf. A000837.
Sequence in context: A068036 A077947 A077972 this_sequence A073118 A048082 A089089
Adjacent sequences: A085407 A085408 A085409 this_sequence A085411 A085412 A085413
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 13 2003
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 17 2003
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