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 A300486 Number of relatively prime or monic partitions of n. 17
 1, 2, 3, 4, 7, 8, 15, 18, 28, 35, 56, 64, 101, 120, 168, 210, 297, 348, 490, 583, 776, 946, 1255, 1482, 1952, 2335, 2981, 3581, 4565, 5387, 6842, 8119, 10086, 12013, 14863, 17527, 21637, 25525, 31083, 36695, 44583, 52256, 63261, 74171, 88932, 104303, 124754 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A relatively prime or monic partition of n is an integer partition of n that is either of length 1 (monic) or whose parts have no common divisor other than 1 (relatively prime). LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1000 A. David Christopher and M. Davamani Christober, Relatively Prime Uniform Partitions, Gen. Math. Notes, Vol. 13, No. 2, December, 2012, pp. 1-12. FORMULA a(n > 1) = 1 + A000837(n) = 1 + Sum_{d|n} mu(d) * A000041(n/d). EXAMPLE The a(6) = 8 relatively prime or monic partitions are (6), (51), (411), (321), (3111), (2211), (21111), (111111). Missing from this list are (42), (33), (222). MATHEMATICA Table[Length[Select[IntegerPartitions[n], Or[Length[#]===1, GCD@@#===1]&]], {n, 20}] PROG (PARI) a(n)={(n > 1) + sumdiv(n, d, moebius(d)*numbpart(n/d))} \\ Andrew Howroyd, Aug 29 2018 CROSSREFS Cf. A000837, A001383, A063834, A093637, A196545, A281113, A289501, A300383, A301462, A301467, A301480, A302094, A302698, A302915, A302916, A302917. Sequence in context: A015927 A097110 A116961 * A120611 A092063 A227007 Adjacent sequences:  A300483 A300484 A300485 * A300487 A300488 A300489 KEYWORD nonn AUTHOR Gus Wiseman, Apr 15 2018 STATUS approved

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Last modified April 4 05:30 EDT 2020. Contains 333212 sequences. (Running on oeis4.)