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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.
7
3, 6, 7, 9, 12, 14, 18, 19, 21, 24, 27, 28, 36, 38, 42, 48, 49, 53, 54, 56, 57, 63, 72, 76, 81, 84, 96, 98, 106, 108, 112, 114, 126, 131, 133, 144, 147, 152, 159, 162, 168, 171, 189, 192, 196, 212, 216, 224, 228, 243, 252, 262, 266, 288, 294, 304, 311, 318
OFFSET
1,1
COMMENTS
Numbers n such that A109082(n) = 2.
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.
Also Heinz numbers of integer partitions into powers of 2 with at least one part > 1 (counted by A102378).
EXAMPLE
The sequence of terms together with their prime indices begins:
3: {2}
6: {1,2}
7: {4}
9: {2,2}
12: {1,1,2}
14: {1,4}
18: {1,2,2}
19: {8}
21: {2,4}
24: {1,1,1,2}
27: {2,2,2}
28: {1,1,4}
36: {1,1,2,2}
38: {1,8}
42: {1,2,4}
48: {1,1,1,1,2}
49: {4,4}
53: {16}
54: {1,2,2,2}
56: {1,1,1,4}
MATHEMATICA
Select[Range[100], And[!IntegerQ[Log[2, #]], And@@Cases[FactorInteger[#], {p_, _}:>IntegerQ[Log[2, PrimePi[p]]]]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 21 2019
STATUS
approved