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%I #9 Sep 08 2018 12:07:01
%S 3,5,7,9,11,13,17,19,21,23,25,27,29,31,37,39,41,43,47,49,53,57,59,61,
%T 63,65,67,71,73,79,81,83,87,89,91,97,101,103,107,109,111,113,115,117,
%U 121,125,127,129,131,133,137,139,147,149,151,157,159,163,167,169
%N Heinz numbers of integer partitions with a common divisor > 1.
%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C Is this the same as A305078 without the leading 2? - _R. J. Mathar_, Sep 08 2018
%e The sequence of all integer partitions with a common divisor begins: (2), (3), (4), (2,2), (5), (6), (7), (8), (4,2), (9), (3,3), (2,2,2), (10), (11), (12), (6,2), (13), (14), (15), (4,4), (16), (8,2), (17), (18), (4,2,2), (6,3), (19), (20), (21), (22), (2,2,2,2), (23), (10,2), (24), (6,4), (25).
%t Select[Range[100],GCD@@PrimePi/@If[#==1,{},FactorInteger[#]][[All,1]]>1&]
%Y Cf. A000837, A018783, A056239, A289508, A289509, A296150, A298748.
%K nonn
%O 1,1
%A _Gus Wiseman_, Sep 06 2018
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