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A316521
Matula-Goebel numbers of rooted trees where all terminal rooted subtrees are either constant or strict.
1
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 38, 39, 41, 42, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 62, 64, 65, 66, 67, 69, 70, 73, 77, 78, 79, 81, 82, 83, 85, 86, 87, 91, 93, 94, 95, 97, 101
OFFSET
1,2
COMMENTS
The following are equivalent.
1. n is in the sequence.
2. prime(n) is in the sequence.
3. n is a product of prime numbers that are already in the sequence and that are either all equal or all different.
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
go[n_]:=And[Or[SameQ@@primeMS[n], UnsameQ@@primeMS[n]], And@@go/@primeMS[n]]
Select[Range[100], go]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 05 2018
STATUS
approved