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%I #28 Aug 29 2018 02:52:13
%S 1,2,3,4,7,8,15,18,28,35,56,64,101,120,168,210,297,348,490,583,776,
%T 946,1255,1482,1952,2335,2981,3581,4565,5387,6842,8119,10086,12013,
%U 14863,17527,21637,25525,31083,36695,44583,52256,63261,74171,88932,104303,124754
%N Number of relatively prime or monic 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).
%H Andrew Howroyd, <a href="/A300486/b300486.txt">Table of n, a(n) for n = 1..1000</a>
%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.
%F a(n > 1) = 1 + A000837(n) = 1 + Sum_{d|n} mu(d) * A000041(n/d).
%e 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).
%t Table[Length[Select[IntegerPartitions[n],Or[Length[#]===1,GCD@@#===1]&]],{n,20}]
%o (PARI) a(n)={(n > 1) + sumdiv(n, d, moebius(d)*numbpart(n/d))} \\ _Andrew Howroyd_, Aug 29 2018
%Y Cf. A000837, A001383, A063834, A093637, A196545, A281113, A289501, A300383, A301462, A301467, A301480, A302094, A302698, A302915, A302916, A302917.
%K nonn
%O 1,2
%A _Gus Wiseman_, Apr 15 2018
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