|
|
A365677
|
|
Number of increasing geometric progressions in {1,2,3,...,n} with rational ratio and length >= 3.
|
|
4
|
|
|
0, 0, 0, 1, 1, 1, 1, 3, 5, 5, 5, 6, 6, 6, 6, 11, 11, 13, 13, 14, 14, 14, 14, 16, 20, 20, 24, 25, 25, 25, 25, 31, 31, 31, 31, 36, 36, 36, 36, 38, 38, 38, 38, 39, 41, 41, 41, 46, 52, 56, 56, 57, 57, 61, 61, 63, 63, 63, 63, 64, 64, 64, 66, 79, 79, 79, 79, 80, 80, 80, 80, 86, 86, 86, 90, 91, 91
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,8
|
|
LINKS
|
|
|
FORMULA
|
a(n) = A366471(n) - n*(1 + (n-1)/2) = Sum_{k=3 .. 1+floor(log_2(n))} Sum_{p=2..floor(n^(1/(k-1)))} phi(p)*floor(n/p^(k-1)), where phi is the Euler phi-function A000010.
|
|
EXAMPLE
|
a(9) = 5 as {1,2,...,9} contains the geometric progressions [1,2,4], [1,2,4,8], [2,4,8], [1,3,9], [4,6,9].
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|