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 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 (list; graph; refs; listen; history; text; internal format)
 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 Michael S. Branicky, Table of n, a(n) for n = 1..10000 Michael S. Branicky, Python Program William Lowell Putman Mathematical Competition, Number 66, 2005, Problem A-1. 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 Cf. A062051, A356792. Sequence in context: A238015 A257679 A056059 * A357900 A357732 A356428 Adjacent sequences: A355912 A355913 A355914 * A355916 A355917 A355918 KEYWORD nonn AUTHOR Michael S. Branicky and N. J. A. Sloane, Sep 21 2022 EXTENSIONS More than the usual number of terms are shown, to distinguish this from similar sequences. STATUS approved

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Last modified September 23 19:57 EDT 2023. Contains 365554 sequences. (Running on oeis4.)