cp's OEIS Frontend

A337450 Number of relatively prime compositions of n with no 1's.

%I A337450 #34 Feb 02 2021 19:07:33
%S A337450 0,0,0,0,0,2,0,7,5,17,17,54,51,143,168,358,482,986,1313,2583,3663,
%T A337450 6698,9921,17710,26489,46352,70928,121137,188220,317810,497322,832039,
%U A337450 1313501,2177282,3459041,5702808,9094377,14930351,23895672,39084070,62721578
%N A337450 Number of relatively prime compositions of n with no 1's.
%C A337450 A composition of n is a finite sequence of positive integers summing to n.
%H A337450 Alois P. Heinz, <a href="/A337450/b337450.txt">Table of n, a(n) for n = 0..2000</a> (first 171 terms from Fausto A. C. Cariboni)
%e A337450 The a(5) = 2 through a(10) = 17 compositions (empty column indicated by dot):
%e A337450   (2,3)  .  (2,5)    (3,5)    (2,7)      (3,7)
%e A337450   (3,2)     (3,4)    (5,3)    (4,5)      (7,3)
%e A337450             (4,3)    (2,3,3)  (5,4)      (2,3,5)
%e A337450             (5,2)    (3,2,3)  (7,2)      (2,5,3)
%e A337450             (2,2,3)  (3,3,2)  (2,2,5)    (3,2,5)
%e A337450             (2,3,2)           (2,3,4)    (3,3,4)
%e A337450             (3,2,2)           (2,4,3)    (3,4,3)
%e A337450                               (2,5,2)    (3,5,2)
%e A337450                               (3,2,4)    (4,3,3)
%e A337450                               (3,4,2)    (5,2,3)
%e A337450                               (4,2,3)    (5,3,2)
%e A337450                               (4,3,2)    (2,2,3,3)
%e A337450                               (5,2,2)    (2,3,2,3)
%e A337450                               (2,2,2,3)  (2,3,3,2)
%e A337450                               (2,2,3,2)  (3,2,2,3)
%e A337450                               (2,3,2,2)  (3,2,3,2)
%e A337450                               (3,2,2,2)  (3,3,2,2)
%p A337450 b:= proc(n, g) option remember; `if`(n=0,
%p A337450      `if`(g=1, 1, 0), add(b(n-j, igcd(g, j)), j=2..n))
%p A337450     end:
%p A337450 a:= n-> b(n, 0):
%p A337450 seq(a(n), n=0..42);
%t A337450 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],!MemberQ[#,1]&&GCD@@#==1&]],{n,0,15}]
%Y A337450 A000740 is the version allowing 1's.
%Y A337450 2*A055684(n) is the case of length 2.
%Y A337450 A302697 ranks the unordered case.
%Y A337450 A302698 is the unordered version.
%Y A337450 A337451 is the strict version.
%Y A337450 A337452 is the unordered strict version.
%Y A337450 A000837 counts relatively prime partitions.
%Y A337450 A002865 counts partitions with no 1's.
%Y A337450 A101268 counts singleton or pairwise coprime compositions.
%Y A337450 A212804 counts compositions with no 1's.
%Y A337450 A291166 appears to rank relatively prime compositions.
%Y A337450 A337462 counts pairwise coprime compositions.
%Y A337450 Cf. A000010, A007359, A023023, A101268, A178472, A289509, A302568, A337485.
%K A337450 nonn
%O A337450 0,6
%A A337450 _Gus Wiseman_, Aug 31 2020