# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a328460 Showing 1-1 of 1 %I A328460 #7 Oct 19 2019 14:45:07 %S A328460 1,1,1,2,2,4,5,8,11,16,26,35,53,76,115,168,244,363,528,782,1144,1685, %T A328460 2474,3633,5347,7844,11539,16946,24919,36605,53782,79053,116142, %U A328460 170700,250800,368585,541610,795884,1169572,1718593,2525522,3711134,5453542,8013798,11776138 %N A328460 Number of compositions of n with no part divisible by the next. %H A328460 Andrew Howroyd, Table of n, a(n) for n = 0..1000 %e A328460 The a(1) = 1 through a(9) = 16 compositions: %e A328460 (1) (2) (3) (4) (5) (6) (7) (8) (9) %e A328460 (21) (31) (23) (42) (25) (35) (27) %e A328460 (32) (51) (34) (53) (45) %e A328460 (41) (231) (43) (62) (54) %e A328460 (321) (52) (71) (63) %e A328460 (61) (251) (72) %e A328460 (232) (323) (81) %e A328460 (421) (341) (234) %e A328460 (431) (252) %e A328460 (521) (342) %e A328460 (2321) (351) %e A328460 (423) %e A328460 (432) %e A328460 (531) %e A328460 (621) %e A328460 (3231) %t A328460 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],!MatchQ[#,{___,x_,y_,___}/;Divisible[y,x]]&]],{n,0,10}] %o A328460 (PARI) seq(n)={my(r=matid(n)); for(k=1, n, for(i=1, k-1, r[i,k]=sum(j=1, k-i, if(j%i, r[j, k-i])))); concat([1], vecsum(Col(r)))} \\ _Andrew Howroyd_, Oct 19 2019 %Y A328460 The case of partitions is A328171. %Y A328460 If we also require no part to be divisible by the prior, we get A328508. %Y A328460 Compositions with each part relatively prime to the next are A167606. %Y A328460 Compositions with no part relatively prime to the next are A178470. %Y A328460 Cf. A328026, A328028, A328161, A328172, A328189. %K A328460 nonn %O A328460 0,4 %A A328460 _Gus Wiseman_, Oct 17 2019 %E A328460 Terms a(26) and beyond from _Andrew Howroyd_, Oct 19 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE