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A324927 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.

%I A324927 #5 Mar 21 2019 17:22:06
%S A324927 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 A324927 81,84,96,98,106,108,112,114,126,131,133,144,147,152,159,162,168,171,
%U A324927 189,192,196,212,216,224,228,243,252,262,266,288,294,304,311,318
%N A324927 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 A324927 Numbers n such that A109082(n) = 2.
%C A324927 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 A324927 Also Heinz numbers of integer partitions into powers of 2 with at least one part > 1 (counted by A102378).
%e A324927 The sequence of terms together with their prime indices begins:
%e A324927    3: {2}
%e A324927    6: {1,2}
%e A324927    7: {4}
%e A324927    9: {2,2}
%e A324927   12: {1,1,2}
%e A324927   14: {1,4}
%e A324927   18: {1,2,2}
%e A324927   19: {8}
%e A324927   21: {2,4}
%e A324927   24: {1,1,1,2}
%e A324927   27: {2,2,2}
%e A324927   28: {1,1,4}
%e A324927   36: {1,1,2,2}
%e A324927   38: {1,8}
%e A324927   42: {1,2,4}
%e A324927   48: {1,1,1,1,2}
%e A324927   49: {4,4}
%e A324927   53: {16}
%e A324927   54: {1,2,2,2}
%e A324927   56: {1,1,1,4}
%t A324927 Select[Range[100],And[!IntegerQ[Log[2,#]],And@@Cases[FactorInteger[#],{p_,_}:>IntegerQ[Log[2,PrimePi[p]]]]]&]
%Y A324927 Cf. A000081, A000720, A003963, A007097, A018819, A033844, A056239, A102378, A112798, A302242, A318400, A324928, A324929.
%K A324927 nonn
%O A324927 1,1
%A A324927 _Gus Wiseman_, Mar 21 2019