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A337984 Heinz numbers of pairwise coprime integer partitions with no 1's, where a singleton is not considered coprime.

%I A337984 #5 Nov 01 2020 01:46:49
%S A337984 15,33,35,51,55,69,77,85,93,95,119,123,141,143,145,155,161,165,177,
%T A337984 187,201,205,209,215,217,219,221,249,253,255,265,287,291,295,309,323,
%U A337984 327,329,335,341,355,381,385,391,395,403,407,411,413,415,437,447,451,465
%N A337984 Heinz numbers of pairwise coprime integer partitions with no 1's, where a singleton is not considered coprime.
%C A337984 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions.
%F A337984 Equals A302568\A000040.
%e A337984 The sequence of terms together with their prime indices begins:
%e A337984      15: {2,3}     155: {3,11}     265: {3,16}
%e A337984      33: {2,5}     161: {4,9}      287: {4,13}
%e A337984      35: {3,4}     165: {2,3,5}    291: {2,25}
%e A337984      51: {2,7}     177: {2,17}     295: {3,17}
%e A337984      55: {3,5}     187: {5,7}      309: {2,27}
%e A337984      69: {2,9}     201: {2,19}     323: {7,8}
%e A337984      77: {4,5}     205: {3,13}     327: {2,29}
%e A337984      85: {3,7}     209: {5,8}      329: {4,15}
%e A337984      93: {2,11}    215: {3,14}     335: {3,19}
%e A337984      95: {3,8}     217: {4,11}     341: {5,11}
%e A337984     119: {4,7}     219: {2,21}     355: {3,20}
%e A337984     123: {2,13}    221: {6,7}      381: {2,31}
%e A337984     141: {2,15}    249: {2,23}     385: {3,4,5}
%e A337984     143: {5,6}     253: {5,9}      391: {7,9}
%e A337984     145: {3,10}    255: {2,3,7}    395: {3,22}
%t A337984 Select[Range[1,100,2],SquareFreeQ[#]&&CoprimeQ@@PrimePi/@First/@FactorInteger[#]&]
%Y A337984 A005117 is a superset.
%Y A337984 A337485 counts these partitions.
%Y A337984 A302568 considers singletons to be coprime.
%Y A337984 A304711 allows 1's, with squarefree version A302797.
%Y A337984 A337694 is the pairwise non-coprime instead of pairwise coprime version.
%Y A337984 A007359 counts partitions into singleton or pairwise coprime parts with no 1's
%Y A337984 A101268 counts pairwise coprime or singleton compositions, ranked by A335235.
%Y A337984 A305713 counts pairwise coprime strict partitions.
%Y A337984 A327516 counts pairwise coprime partitions, ranked by A302696.
%Y A337984 A337462 counts pairwise coprime compositions, ranked by A333227.
%Y A337984 A337561 counts pairwise coprime strict compositions.
%Y A337984 A337665 counts compositions whose distinct parts are pairwise coprime, ranked by A333228.
%Y A337984 A337667 counts pairwise non-coprime compositions, ranked by A337666.
%Y A337984 A337697 counts pairwise coprime compositions with no 1's.
%Y A337984 A337983 counts pairwise non-coprime strict compositions, with unordered version A318717 ranked by A318719.
%Y A337984 Cf. A051424, A056239, A087087, A112798, A200976, A220377, A302569, A303140, A303282, A328673, A328867.
%K A337984 nonn
%O A337984 1,1
%A A337984 _Gus Wiseman_, Oct 22 2020