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A326646 Heinz numbers of non-constant integer partitions whose mean and geometric mean are both integers.

%I A326646 #5 Jul 16 2019 22:02:23
%S A326646 46,57,183,194,228,371,393,454,515,687,742,838,1057,1064,1077,1150,
%T A326646 1157,1159,1244,1322,1563,1895,2018,2060,2116,2157,2163,2167,2177,
%U A326646 2225,2231,2405,2489,2854,2859,3249,3263,3339,3352,3558,3669,3758,3787,3914,4265,4351
%N A326646 Heinz numbers of non-constant integer partitions whose mean and geometric mean are both integers.
%C A326646 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A326646 The enumeration of these partitions by sum is given by A326642.
%H A326646 Wikipedia, <a href="https://en.wikipedia.org/wiki/Geometric_mean">Geometric mean</a>
%e A326646 The sequence of terms together with their prime indices begins:
%e A326646     46: {1,9}
%e A326646     57: {2,8}
%e A326646    183: {2,18}
%e A326646    194: {1,25}
%e A326646    228: {1,1,2,8}
%e A326646    371: {4,16}
%e A326646    393: {2,32}
%e A326646    454: {1,49}
%e A326646    515: {3,27}
%e A326646    687: {2,50}
%e A326646    742: {1,4,16}
%e A326646    838: {1,81}
%e A326646   1057: {4,36}
%e A326646   1064: {1,1,1,4,8}
%e A326646   1077: {2,72}
%e A326646   1150: {1,3,3,9}
%e A326646   1157: {6,24}
%e A326646   1159: {8,18}
%e A326646   1244: {1,1,64}
%e A326646   1322: {1,121}
%Y A326646 Heinz numbers of partitions with integer mean and geometric mean are A326645.
%Y A326646 Heinz numbers of partitions with integer mean are A316413.
%Y A326646 Heinz numbers of partitions with integer geometric mean are A326623.
%Y A326646 Non-constant partitions with integer mean and geometric mean are A326642.
%Y A326646 Subsets with integer mean and geometric mean are A326643.
%Y A326646 Strict partitions with integer mean and geometric mean are A326029.
%Y A326646 Cf. A051293, A067538, A067539, A078175, A082553, A102627, A326027, A326641, A326644, A326647.
%K A326646 nonn
%O A326646 1,1
%A A326646 _Gus Wiseman_, Jul 16 2019