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A209638 Sequence A209636 (or A209637) sorted into ascending order.

%I A209638 #28 May 04 2021 17:40:31
%S A209638 1,2,3,4,5,6,7,8,10,11,12,13,14,16,17,19,20,22,24,26,28,29,31,32,34,
%T A209638 37,38,40,41,43,44,48,52,53,56,58,59,62,64,67,68,71,74,76,79,80,82,86,
%U A209638 88,89,96,101,104,106,107,109,112,116,118,124,127,128,131,134
%N A209638 Sequence A209636 (or A209637) sorted into ascending order.
%C A209638 These are Matula-numbers (see A061773) for the rooted trees where no vertices with more than one non-leaf branch ever occur. In other words, natural numbers which are either some power of 2, or of the form 2^k * p_i, where k >= 0, and p_i is the i-th prime (A000040(i)), with i being one of the terms of this sequence.
%H A209638 <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>
%o A209638 (Python)
%o A209638 from sympy import prime
%o A209638 def a(n):
%o A209638     n = 2*n
%o A209638     m = 1
%o A209638     if n<2: return 1
%o A209638     while n>1:
%o A209638         if n%2==0:
%o A209638             n//=2
%o A209638             m*=2
%o A209638         else:
%o A209638             n=(n - 1)//2
%o A209638             m=prime(m)
%o A209638     return m
%o A209638 print(sorted([a(n) for n in range(101)])) # _Indranil Ghosh_, May 26 2017
%Y A209638 Sorted version of A209636 and A209637.
%Y A209638 Subset of A093641 and A122132.
%K A209638 nonn
%O A209638 0,2
%A A209638 _Antti Karttunen_, Mar 11 2012