cp's OEIS Frontend

A337451 Number of relatively prime strict compositions of n with no 1's.

%I A337451 #28 Feb 01 2021 17:50:33
%S A337451 0,0,0,0,0,2,0,4,2,10,8,20,14,34,52,72,90,146,172,244,390,502,680,956,
%T A337451 1218,1686,2104,3436,4078,5786,7200,10108,12626,17346,20876,32836,
%U A337451 38686,53674,67144,91528,113426,152810,189124,245884,343350,428494,552548,719156
%N A337451 Number of relatively prime strict compositions of n with no 1's.
%C A337451 A strict composition of n is a finite sequence of distinct positive integers summing to n.
%H A337451 Fausto A. C. Cariboni, <a href="/A337451/b337451.txt">Table of n, a(n) for n = 0..350</a>
%e A337451 The a(5) = 2 through a(10) = 8 compositions (empty column indicated by dot):
%e A337451   (2,3)  .  (2,5)  (3,5)  (2,7)    (3,7)
%e A337451   (3,2)     (3,4)  (5,3)  (4,5)    (7,3)
%e A337451             (4,3)         (5,4)    (2,3,5)
%e A337451             (5,2)         (7,2)    (2,5,3)
%e A337451                           (2,3,4)  (3,2,5)
%e A337451                           (2,4,3)  (3,5,2)
%e A337451                           (3,2,4)  (5,2,3)
%e A337451                           (3,4,2)  (5,3,2)
%e A337451                           (4,2,3)
%e A337451                           (4,3,2)
%t A337451 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@#&&!MemberQ[#,1]&&GCD@@#==1&]],{n,0,15}]
%Y A337451 A032022 does not require relative primality.
%Y A337451 A302698 is the unordered non-strict version.
%Y A337451 A332004 is the version allowing 1's.
%Y A337451 A337450 is the non-strict version.
%Y A337451 A337452 is the unordered version.
%Y A337451 A000837 counts relatively prime partitions.
%Y A337451 A032020 counts strict compositions.
%Y A337451 A078374 counts strict relatively prime partitions.
%Y A337451 A002865 counts partitions with no 1's.
%Y A337451 A212804 counts compositions with no 1's.
%Y A337451 A291166 appears to rank relatively prime compositions.
%Y A337451 A337462 counts pairwise coprime compositions.
%Y A337451 A337561 counts strict pairwise coprime compositions.
%Y A337451 Cf. A000010, A007359, A101268, A178472, A216652, A289509, A337562, A337563.
%K A337451 nonn
%O A337451 0,6
%A A337451 _Gus Wiseman_, Aug 31 2020