login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A123323 Number of integer-sided triangles with maximum side n, with sides relatively prime. 7
1, 1, 3, 4, 8, 7, 15, 14, 21, 20, 35, 26, 48, 39, 52, 52, 80, 57, 99, 76, 102, 95, 143, 100, 160, 132, 171, 150, 224, 148, 255, 200, 250, 224, 300, 222, 360, 279, 348, 296, 440, 294, 483, 370, 444, 407, 575, 392, 609, 460, 592, 516, 728, 495, 740, 588, 738, 644 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Number of triples a,b,c with a <= b <= c < a+b, gcd(a,b,c) = 1 and c = n.

Dropping the requirement for side lengths to be relatively prime this sequence becomes A002620 (with a different offset). See the Sep 2006 comment in A002620. - Peter Munn, Jul 26 2017

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Stackexchange, Number of triplets for which gcd(a,b,c)=1 and c=n, Feb 25 2014

FORMULA

Moebius transform of b(n) = floor((n+1)^2/4).

G.f.: (G(x)+x-x^2)/2, where G(x) = Sum_{k >= 1} mobius(k)*x^k*(1+2*x^k-x^(2*k))/(1-x^k)^2/(1-x^(2*k)).

MAPLE

with(numtheory):

a:= n-> add(mobius(n/d)*floor((d+1)^2/4), d=divisors(n)):

seq(a(n), n=1..60);  # Alois P. Heinz, Oct 23 2013

MATHEMATICA

a[n_] := DivisorSum[n, Floor[(#+1)^2/4]*MoebiusMu[n/#]&]; Array[a, 60] (* Jean-Fran├žois Alcover, Dec 07 2015 *)

PROG

(PARI) A123323(n)=sumdiv(n, d, floor((d+1)^2/4)*moebius(n/d)).

CROSSREFS

Cf. A002620, A051493, A054875, A070110, A123324, A123325.

Sequence in context: A049826 A310014 A310015 * A034772 A197138 A065309

Adjacent sequences:  A123320 A123321 A123322 * A123324 A123325 A123326

KEYWORD

easy,look,nonn

AUTHOR

Franklin T. Adams-Watters, Sep 25 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 17 12:09 EST 2018. Contains 317276 sequences. (Running on oeis4.)