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

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, 37, 38, 40, 41, 43, 44, 48, 52, 53, 56, 58, 59, 62, 64, 67, 68, 71, 74, 76, 79, 80, 82, 86, 88, 89, 96, 101, 104, 106, 107, 109, 112, 116, 118, 124, 127, 128, 131, 134

Offset: 0

Author

Antti Karttunen, Mar 11 2012

Keywords

• nonn

Comments

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.

Links

• Index entries for sequences related to Matula-Goebel numbers

Crossrefs

Sorted version of A209636 and A209637.

Subset of A093641 and A122132.

Programs

Python

from sympy import prime
def a(n):
    n = 2*n
    m = 1
    if n<2: return 1
    while n>1:
        if n%2==0:
            n//=2
            m*=2
        else:
            n=(n - 1)//2
            m=prime(m)
    return m
print(sorted([a(n) for n in range(101)])) # Indranil Ghosh, May 26 2017