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%I #5 Mar 21 2019 17:22:06
%S 3,6,7,9,12,14,18,19,21,24,27,28,36,38,42,48,49,53,54,56,57,63,72,76,
%T 81,84,96,98,106,108,112,114,126,131,133,144,147,152,159,162,168,171,
%U 189,192,196,212,216,224,228,243,252,262,266,288,294,304,311,318
%N Matula-Goebel numbers of rooted trees of depth 2. Numbers that are not powers of 2 but whose prime indices are all powers of 2.
%C Numbers n such that A109082(n) = 2.
%C A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C Also Heinz numbers of integer partitions into powers of 2 with at least one part > 1 (counted by A102378).
%e The sequence of terms together with their prime indices begins:
%e 3: {2}
%e 6: {1,2}
%e 7: {4}
%e 9: {2,2}
%e 12: {1,1,2}
%e 14: {1,4}
%e 18: {1,2,2}
%e 19: {8}
%e 21: {2,4}
%e 24: {1,1,1,2}
%e 27: {2,2,2}
%e 28: {1,1,4}
%e 36: {1,1,2,2}
%e 38: {1,8}
%e 42: {1,2,4}
%e 48: {1,1,1,1,2}
%e 49: {4,4}
%e 53: {16}
%e 54: {1,2,2,2}
%e 56: {1,1,1,4}
%t Select[Range[100],And[!IntegerQ[Log[2,#]],And@@Cases[FactorInteger[#],{p_,_}:>IntegerQ[Log[2,PrimePi[p]]]]]&]
%Y Cf. A000081, A000720, A003963, A007097, A018819, A033844, A056239, A102378, A112798, A302242, A318400, A324928, A324929.
%K nonn
%O 1,1
%A _Gus Wiseman_, Mar 21 2019
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