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 A302094 Number of relatively prime or monic twice-partitions of n. 4
 1, 3, 6, 10, 27, 35, 113, 170, 396, 641, 1649, 2318, 5905, 9112, 18678, 32529, 69094, 106210, 227480, 363433, 705210, 1196190, 2325023, 3724233, 7192245, 11915884, 21857887, 36597843, 67406158, 109594872, 201747847, 333400746, 591125465, 987069077, 1743223350 (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). Then a relatively prime or monic twice-partition of n is a choice of a relatively prime or monic partition of each part in a relatively prime or monic partition of n. LINKS Table of n, a(n) for n=1..35. A. David Christopher and M. Davamani Christober, Relatively Prime Uniform Partitions, Gen. Math. Notes, Vol. 13, No. 2, December, 2012, pp. 1-12. EXAMPLE The a(4) = 10 relatively prime or monic twice-partitions: (4), (31), (211), (1111), (3)(1), (21)(1), (111)(1), (2)(1)(1), (11)(1)(1), (1)(1)(1)(1). MATHEMATICA ip[n_]:=ip[n]=Select[IntegerPartitions[n], Or[Length[#]===1, GCD@@#===1]&]; Table[Sum[Times@@Length/@ip/@ptn, {ptn, ip[n]}], {n, 10}] CROSSREFS Cf. A000837, A001383, A063834, A093637, A196545, A281113, A289501, A300383, A300486, A301462, A301467, A301480, A302915, A302916, A302917. Sequence in context: A048006 A364170 A211231 * A068818 A068866 A137173 Adjacent sequences: A302091 A302092 A302093 * A302095 A302096 A302097 KEYWORD nonn AUTHOR Gus Wiseman, Apr 15 2018 STATUS approved

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Last modified August 13 16:51 EDT 2024. Contains 375144 sequences. (Running on oeis4.)