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