OFFSET
1,2
COMMENTS
Let prime(1)=2, ... denote the primes. The label f(T) for a rooted tree T is 1 if T has 1 node, otherwise f(T) = Product prime(f(T_i)) where the T_i are the subtrees obtained by deleting the root and the edges adjacent to it.
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
F. Goebel, On a 1-1-correspondence between rooted trees and natural numbers, J. Combin. Theory, B, Vol. 29, No. 1 (1980), pp. 141-143.
I. Gutman and A. Ivić, Graphs with maximal and minimal Matula numbers, Bulletin CVII Acad. Serbe, Sciences Math., Vol. 107, No. 19 (1994), pp. 65-74.
I. Gutman and A. Ivić, On Matula numbers, Discrete Math., Vol. 150, No. 1-3 (1996), pp. 131-142.
D. W. Matula, A natural rooted tree enumeration by prime factorization, SIAM Rev., Vol. 10 (1968), p. 273.
FORMULA
a(1)=1; a(2)=2; a(3)=4; a(4)=8; a(n) = the a(n-1)-th prime (see the Gutman and Ivic 1994 paper). - Emeric Deutsch, Apr 15 2012
Under plausible assumptions about the growth of the primes, for n >= 4, a(n+1) = a(n)-th prime and A005518(n) = A057452(n-3). - David W. Wilson, Jul 09 2001
MAPLE
with(numtheory): a := proc (n) if n = 1 then 1 elif n = 2 then 2 elif n = 3 then 4 elif n = 4 then 8 else ithprime(a(n-1)) end if end proc: seq(a(n), n = 1 .. 12); # Emeric Deutsch, Apr 15 2012
MATHEMATICA
a[n_] := a[n] = Switch[n, 1, 1, 2, 2, 3, 4, 4, 8, _, Prime[a[n-1]]]; Table[a[n], {n, 1, 16}] (* Jean-François Alcover, Mar 06 2014, after Emeric Deutsch *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from David W. Wilson, Jul 09 2001
a(17)-a(19) from Robert G. Wilson v, Mar 07 2017 using Kim Walisch's primecount
STATUS
approved