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A347820
Least positive integer k such that k*n is a balanced-parentheses number (A014486).
0
2, 1, 4, 3, 2, 2, 6, 7, 20, 1, 4, 1, 4, 3, 12, 15, 10, 10, 12, 9, 2, 2, 8, 9, 2, 2, 8, 2, 8, 6, 22, 31, 84, 5, 6, 5, 20, 6, 24, 6, 18, 1, 4, 1, 4, 4, 16, 5, 56, 1, 4, 1, 4, 4, 16, 1, 4, 4, 16, 3, 16, 11, 44, 63, 42, 42, 56, 3, 10, 3, 12, 3, 40, 10, 44, 3, 36
OFFSET
1,1
COMMENTS
The sequence is well defined, since n divides (2^phi(n) - 1)*2^phi(n), where phi is the Euler phi-function, and this latter number looks like 11...100....0.
EXAMPLE
For n=9, we have a(n)=20, and 9*20=180 in base 2 is 10110100, which represents a balanced-parentheses string.
CROSSREFS
Cf. A014486.
Sequence in context: A355808 A080079 A341707 * A318569 A336280 A362806
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Sep 25 2021
STATUS
approved