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%I #25 Jan 31 2021 17:54:39
%S 0,0,0,0,0,1,0,2,1,3,2,6,3,9,7,11,11,20,15,28,24,35,36,55,47,73,71,95,
%T 96,136,123,180,177,226,235,305,299,403,406,503,523,668,662,852,873,
%U 1052,1115,1370,1391,1720,1784,2125,2252,2701,2786,3348,3520,4116
%N Number of relatively prime strict integer partitions of n with no 1's.
%H Fausto A. C. Cariboni, <a href="/A337452/b337452.txt">Table of n, a(n) for n = 0..300</a>
%e The a(5) = 1 through a(16) = 11 partitions (A = 10, B = 11, C = 12, D = 13):
%e 32 43 53 54 73 65 75 76 95 87 97
%e 52 72 532 74 543 85 B3 B4 B5
%e 432 83 732 94 653 D2 D3
%e 92 A3 743 654 754
%e 542 B2 752 753 763
%e 632 643 932 762 853
%e 652 5432 843 943
%e 742 852 952
%e 832 942 B32
%e A32 6532
%e 6432 7432
%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&!MemberQ[#,1]&&GCD@@#==1&]],{n,0,15}]
%Y A078374 is the version allowing 1's.
%Y A302698 is the non-strict version.
%Y A332004 is the ordered version allowing 1's.
%Y A337450 is the ordered non-strict version.
%Y A337451 is the ordered version.
%Y A337485 is the pairwise coprime version.
%Y A000837 counts relatively prime partitions.
%Y A078374 counts relatively prime strict partitions.
%Y A002865 counts partitions with no 1's.
%Y A212804 counts compositions with no 1's.
%Y A291166 appears to rank relatively prime compositions.
%Y A337561 counts pairwise coprime strict compositions.
%Y Cf. A007359, A101268, A289509, A337485, A337563.
%K nonn
%O 0,8
%A _Gus Wiseman_, Aug 31 2020
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