A347820 - OEIS

A347820

Least positive integer k such that k*n is a balanced-parentheses number (A014486).

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

(list; graph; refs; listen; history; text; internal format)

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.

LINKS

Table of n, a(n) for n=1..77.

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

Adjacent sequences: A347817 A347818 A347819 * A347821 A347822 A347823

KEYWORD

nonn

AUTHOR

Jeffrey Shallit, Sep 25 2021

STATUS

approved