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A316438 Heinz numbers of integer partitions whose product is strictly greater than the LCM of the parts.

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%I A316438 #6 Jul 04 2018 20:24:27
%S A316438 9,18,21,25,27,36,39,42,45,49,50,54,57,63,65,72,75,78,81,84,87,90,91,
%T A316438 98,99,100,105,108,111,114,115,117,121,125,126,129,130,133,135,144,
%U A316438 147,150,153,156,159,162,168,169,171,174,175,180,182,183,185,189,195
%N A316438 Heinz numbers of integer partitions whose product is strictly greater than the LCM of the parts.
%C A316438 Also numbers n > 1 such that A290104(n) > 1.
%C A316438 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e A316438 Sequence of partitions whose product is greater than their LCM begins: (22), (221), (42), (33), (222), (2211), (62), (421), (322), (44), (331), (2221), (82), (422), (63), (22111), (332), (621), (2222), (4211).
%t A316438 Select[Range[2,300],With[{pms=Flatten[Cases[FactorInteger[#],{p_,k_}:>Table[PrimePi[p],{k}]]]},Times@@pms/LCM@@pms>1]&]
%Y A316438 Cf. A056239, A074761, A143773, A285572, A289508, A290103, A296150, A316429, A316431, A316433, A316437.
%K A316438 nonn
%O A316438 1,1
%A A316438 _Gus Wiseman_, Jul 03 2018