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A120486 Partial sums of A000188. 6
1, 2, 3, 5, 6, 7, 8, 10, 13, 14, 15, 17, 18, 19, 20, 24, 25, 28, 29, 31, 32, 33, 34, 36, 41, 42, 45, 47, 48, 49, 50, 54, 55, 56, 57, 63, 64, 65, 66, 68, 69, 70, 71, 73, 76, 77, 78, 82, 89, 94, 95, 97, 98, 101, 102, 104, 105, 106, 107, 109, 110, 111, 114, 122, 123, 124, 125, 127, 128 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence can also be described as the number of 3-term nondecreasing geometric progressions with no term exceeding n.

a(n) = A132188(n) - A132345(n). - Reinhard Zumkeller, Apr 21 2012

LINKS

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

Vaclav Kotesovec, Graph - the asymptotic ratio

Gerry Myerson, Trifectas in Geometric Progression, Australian Mathematical Society Gazette, 35 (3) 2008, p 189-194.

FORMULA

a(n) = 3n log(n) / Pi^2 + O(n). - Griffin N. Macris, Jan 28 2017

a(n) ~ 3*n*((log(n) + (3*gamma - 1))/ Pi^2 - 12*(Zeta'(2)/Pi^4)), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jan 30 2019

a(n) = Sum_{k=1..n} phi(k)*floor(n/k^2), where phi is the Euler totient function A000010. - Ridouane Oudra, Aug 18 2019

MAPLE

with(numtheory): seq(add(phi(k)*floor(n/k^2), k=1..n), n=1..100); # Ridouane Oudra, Aug 18 2019

PROG

(Haskell)

a120486 n = a120486_list !! (n - 1)

a120486_list = scanl1 (+) a000188_list

-- Reinhard Zumkeller, Apr 22 2012

CROSSREFS

Cf. A000188, A132188, A132189.

Sequence in context: A028748 A028783 A274779 * A229993 A323252 A219255

Adjacent sequences:  A120483 A120484 A120485 * A120487 A120488 A120489

KEYWORD

nonn

AUTHOR

Gerry Myerson, Nov 21 2007

STATUS

approved

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Last modified April 16 05:26 EDT 2021. Contains 343030 sequences. (Running on oeis4.)