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A023023 Number of partitions of n into 3 unordered relatively prime parts. 2
1, 1, 2, 2, 4, 4, 6, 6, 10, 8, 14, 12, 16, 16, 24, 18, 30, 24, 32, 30, 44, 32, 50, 42, 54, 48, 70, 48, 80, 64, 80, 72, 96, 72, 114, 90, 112, 96, 140, 96, 154, 120, 144, 132, 184, 128, 196, 150, 192, 168, 234, 162, 240, 192, 240, 210, 290, 192, 310, 240, 288, 256, 336, 240, 374 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,3

LINKS

Table of n, a(n) for n=3..67.

Mohamed El Bachraoui, Partitions with relatively prime parts [From Jonathan Sondow, May 27 2009]

FORMULA

G.f. for the number of partitions of n into m unordered relatively prime parts is Sum(moebius(k)*x^(m*k)/Product(1-x^(i*k), i=1..m), k=1..infinity). - Vladeta Jovovic, Dec 21 2004

a(n) = (n^2/12)*Product_{prime p|n} (1 - 1/p^2) for n > 3 (proved by Mohamed El Bachraoui). [From Jonathan Sondow, May 27 2009]

CROSSREFS

Cf. A023022-A023030, A000741-A000743, A023031-A023035, A101271.

Sequence in context: A001362 A001310 A029009 * A184157 A008643 A008644

Adjacent sequences:  A023020 A023021 A023022 * A023024 A023025 A023026

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified October 15 19:25 EDT 2019. Contains 328037 sequences. (Running on oeis4.)