login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
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