

A355915


Number of ways to write n as a sum of numbers of the form 2^r * 3^s, where r and s are >= 0, and no summand divides another.


2



1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 3, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 1, 3, 3, 2, 1
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OFFSET

1,11


COMMENTS

It is a theorem of Erdos [Erdős] that this representation is always possible.
Without the divisibility constraint the answer is A062051.
See A356792 for when k first appears.


LINKS



EXAMPLE

Illustration of initial terms:
1 = 2^0
2 = 2^1
3 = 3^1
4 = 2^2
5 = 2+3
6 = 2*3
7 = 2^2+3
8 = 2^3
9 = 3^2
10 = 2^2 + 2*3
11 = 2+3^2 = 2^3+3 (this is the first time there are 2 solutions)
12 = 2^2*3
13 = 2^2+3^2
14 = 2^3+2*3
...


PROG

(Python) # see linked program


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS

More than the usual number of terms are shown, to distinguish this from similar sequences.


STATUS

approved



