This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A338318 #11 Nov 05 2020 22:55:15
%S A338318 9,21,25,27,39,49,57,63,65,81,87,91,111,115,117,121,125,129,133,147,
%T A338318 159,169,171,183,185,189,203,213,235,237,243,247,259,261,267,273,289,
%U A338318 299,301,303,305,319,321,325,333,339,343,351,361,365,371,377,387,393
%N A338318 Composite numbers whose prime indices are pairwise intersecting (non-coprime).
%C A338318 First differs from A322336 in lacking 2535, with prime indices {2,3,6,6}.
%C A338318 First differs from A327685 in having 17719, with prime indices {6,10,15}.
%C A338318 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C A338318 Also Heinz numbers of pairwise intersecting (non-coprime) partitions with more than one part. The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), giving a bijective correspondence between positive integers and integer partitions.
%F A338318 Equals A337694 \ A008578.
%e A338318 The sequence of terms together with their prime indices begins:
%e A338318 9: {2,2} 121: {5,5} 243: {2,2,2,2,2}
%e A338318 21: {2,4} 125: {3,3,3} 247: {6,8}
%e A338318 25: {3,3} 129: {2,14} 259: {4,12}
%e A338318 27: {2,2,2} 133: {4,8} 261: {2,2,10}
%e A338318 39: {2,6} 147: {2,4,4} 267: {2,24}
%e A338318 49: {4,4} 159: {2,16} 273: {2,4,6}
%e A338318 57: {2,8} 169: {6,6} 289: {7,7}
%e A338318 63: {2,2,4} 171: {2,2,8} 299: {6,9}
%e A338318 65: {3,6} 183: {2,18} 301: {4,14}
%e A338318 81: {2,2,2,2} 185: {3,12} 303: {2,26}
%e A338318 87: {2,10} 189: {2,2,2,4} 305: {3,18}
%e A338318 91: {4,6} 203: {4,10} 319: {5,10}
%e A338318 111: {2,12} 213: {2,20} 321: {2,28}
%e A338318 115: {3,9} 235: {3,15} 325: {3,3,6}
%e A338318 117: {2,2,6} 237: {2,22} 333: {2,2,12}
%t A338318 stabstrQ[u_,Q_]:=And@@Not/@Q@@@Tuples[u,2];
%t A338318 Select[Range[2,100],!PrimeQ[#]&&stabstrQ[PrimePi/@First/@FactorInteger[#],CoprimeQ]&]
%Y A338318 A200976 counts the partitions with these Heinz numbers.
%Y A338318 A302696 is the pairwise coprime instead of pairwise non-coprime version.
%Y A338318 A337694 includes the primes.
%Y A338318 A002808 lists composite numbers.
%Y A338318 A318717 counts pairwise intersecting strict partitions.
%Y A338318 A328673 counts partitions with pairwise intersecting distinct parts, with Heinz numbers A328867 and restriction to triples A337599 (except n = 3).
%Y A338318 Cf. A008578, A051185, A056239, A101268, A112798, A284825, A302569, A305843, A319752, A327516, A335236, A337666, A337667.
%K A338318 nonn
%O A338318 1,1
%A A338318 _Gus Wiseman_, Oct 31 2020