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A132345 Number of increasing three-term geometric sequences from the integers {1,2,...,n}. 6
0, 0, 0, 1, 1, 1, 1, 2, 4, 4, 4, 5, 5, 5, 5, 8, 8, 10, 10, 11, 11, 11, 11, 12, 16, 16, 18, 19, 19, 19, 19, 22, 22, 22, 22, 27, 27, 27, 27, 28, 28, 28, 28, 29, 31, 31, 31, 34, 40, 44, 44, 45, 45, 47, 47, 48, 48, 48, 48, 49, 49, 49, 51, 58, 58, 58, 58, 59, 59, 59, 59, 64, 64, 64, 68 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

a(n) = A132188(n) - A120486(n); A078147 gives run lengths, apart from initial run of zeros. [Reinhard Zumkeller, Apr 22 2012]

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n)=sum_{1<p^2<=n} phi(p)trunc(n/p^2) where phi is Euler's phi function and trunc is the greatest integer function.

EXAMPLE

a(24)=12 as the sequences counted are 1,2,4; 2,4,8; 3,6,12; 4,8,16; 5,10,20; 6,12,24; 1,3,9; 2,6,18; 4,6,9; 8,12,18; 1,4,16; 9,12,16

MAPLE

sum(numtheory[phi](p)*trunc(n/p^2), p=2..trunc(sqrt(n)));

PROG

(Haskell)

a132345 n = sum $ zipWith (*)

   (tail a000010_list) (map ((div n) . (^ 2)) [2..a000196 n])

-- Reinhard Zumkeller, Apr 22 2012

CROSSREFS

Cf. A000010, A000196, A057918 (first differences).

Sequence in context: A097154 A108421 A104058 * A178976 A130766 A227190

Adjacent sequences:  A132342 A132343 A132344 * A132346 A132347 A132348

KEYWORD

easy,nonn

AUTHOR

David Angell (angell(AT)maths.unsw.edu.au), Nov 07 2007

STATUS

approved

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Last modified June 14 21:27 EDT 2021. Contains 345041 sequences. (Running on oeis4.)