%I #34 Apr 17 2018 03:33:16
%S 1,3,6,10,27,35,113,170,396,641,1649,2318,5905,9112,18678,32529,69094,
%T 106210,227480,363433,705210,1196190,2325023,3724233,7192245,11915884,
%U 21857887,36597843,67406158,109594872,201747847,333400746,591125465,987069077,1743223350
%N Number of relatively prime or monic twice-partitions of n.
%C 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.
%H A. David Christopher and M. Davamani Christober, <a href="http://emis.impa.br/EMIS/journals/GMN/yahoo_site_admin/assets/docs/1_GMN-2492-V13N2.77213831.pdf">Relatively Prime Uniform Partitions</a>, Gen. Math. Notes, Vol. 13, No. 2, December, 2012, pp. 1-12.
%e The a(4) = 10 relatively prime or monic twice-partitions:
%e (4), (31), (211), (1111),
%e (3)(1), (21)(1), (111)(1),
%e (2)(1)(1), (11)(1)(1),
%e (1)(1)(1)(1).
%t ip[n_]:=ip[n]=Select[IntegerPartitions[n],Or[Length[#]===1,GCD@@#===1]&];
%t Table[Sum[Times@@Length/@ip/@ptn,{ptn,ip[n]}],{n,10}]
%Y Cf. A000837, A001383, A063834, A093637, A196545, A281113, A289501, A300383, A300486, A301462, A301467, A301480, A302915, A302916, A302917.
%K nonn
%O 1,2
%A _Gus Wiseman_, Apr 15 2018