# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a328171 Showing 1-1 of 1 %I A328171 #13 Jan 10 2021 08:54:44 %S A328171 1,1,1,1,1,2,1,3,2,4,4,5,4,9,9,10,12,14,16,20,23,29,34,38,41,51,60,66, %T A328171 78,89,103,119,137,157,180,201,229,261,298,338,379,431,486,547,618, %U A328171 694,783,876,986,1103,1241,1387,1551,1728,1932,2148,2395,2664,2963 %N A328171 Number of (necessarily strict) integer partitions of n with no two consecutive parts divisible. %H A328171 Fausto A. C. Cariboni, Table of n, a(n) for n = 0..330 %e A328171 The a(1) = 1 through a(15) = 10 partitions (A..F = 10..15): %e A328171 1 2 3 4 5 6 7 8 9 A B C D E F %e A328171 32 43 53 54 64 65 75 76 86 87 %e A328171 52 72 73 74 543 85 95 96 %e A328171 432 532 83 732 94 A4 B4 %e A328171 92 A3 B3 D2 %e A328171 B2 653 654 %e A328171 643 743 753 %e A328171 652 752 852 %e A328171 832 5432 A32 %e A328171 6432 %t A328171 Table[Length[Select[IntegerPartitions[n],!MatchQ[#,{___,x_,y_,___}/;Divisible[x,y]]&]],{n,0,30}] %Y A328171 The complement is counted by A328221. %Y A328171 The Heinz numbers of these partitions are A328603. %Y A328171 Partitions whose pairs of consecutive parts are relatively prime are A328172, with strict case A328188. %Y A328171 Partitions with no pair of consecutive parts relatively prime are A328187, with strict case A328220. %Y A328171 Numbers without consecutive divisible proper divisors are A328028. %Y A328171 Cf. A000837, A018783, A328026, A328161, A328189, A328194, A328195. %K A328171 nonn %O A328171 0,6 %A A328171 _Gus Wiseman_, Oct 11 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE