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%I #4 Dec 02 2020 20:59:22
%S 1,0,1,1,3,3,7,8,14,16,28,31,51,58,85,103,150,171,247,289,391,468,631,
%T 737,981,1160,1496,1784,2290,2684,3430,4050,5054,5991,7445,8750,10835,
%U 12741,15560,18328,22315,26100,31658,37058,44497,52111,62415,72708,86801,101063
%N Number of partitions of n into an odd number of relatively prime parts.
%C Moebius transform of A027193.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{d|n} mu(n/d) * A027193(d).
%e a(6) = 3 because we have [4, 1, 1], [3, 2, 1] and [2, 1, 1, 1, 1].
%t Table[Sum[MoebiusMu[n/d] Length@Select[IntegerPartitions[d], OddQ[Length@#] &], {d, Divisors[n]}], {n, 1, 50}]
%Y Cf. A000837, A027193, A339397.
%K nonn
%O 1,5
%A _Ilya Gutkovskiy_, Dec 02 2020