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A318151 e-numbers of unlabeled rooted trees with empty leaves o[] allowed. A number n is in the sequence iff n = 2^(prime(y_1) * ... * prime(y_k)) for some k >= 0 and y_1, ..., y_k already in the sequence. 1
1, 2, 4, 8, 16, 64, 128, 256, 512, 4096, 16384, 65536, 262144, 524288, 2097152, 16777216, 134217728, 268435456, 4294967296, 68719476736, 274877906944, 4398046511104, 281474976710656, 562949953421312, 9007199254740992, 18014398509481984, 72057594037927936 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
If n = 1 let e(n) be the leaf symbol "o". Given a positive integer n > 1 we construct a unique orderless expression e(n) (as can be represented in functional programming languages such as Mathematica) with one atom by expressing n as a power of a number that is not a perfect power to a product of prime numbers: n = rad(x)^(prime(y_1) * ... * prime(y_k)) where rad = A007916. Then e(n) = e(x)[e(y_1), ..., e(y_k)]. For example, e(21025) = o[o[o]][o] because 21025 = rad(rad(1)^prime(rad(1)^prime(1)))^prime(1). The sequence consists of all numbers n such that e(n) contains no subexpressions in heads f[x_1, ..., x_k][y_1, ..., y_k] where k,j >= 0.
LINKS
CROSSREFS
A subsequence of A000079.
Sequence in context: A041013 A018754 A264980 * A076086 A246907 A074700
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 19 2018
STATUS
approved

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Last modified May 28 01:34 EDT 2024. Contains 372900 sequences. (Running on oeis4.)