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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A270417 Number of integer-sided right-angled triangles with semiperimeter n. 1
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 3, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 3, 0, 0, 0, 1, 0, 3, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,30

COMMENTS

Number of positive integer solutions to x*y*(y+z)=n with y and z coprime and of opposite parity and z<y.

Records occur at 1, 6, 30, 60, 120, 210, 360, 420, 840, 1260, 2310, 2520, 4620, 9240, 13860, 27720, 55440, 60060, ... - Antti Karttunen, Sep 25 2018

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

EXAMPLE

a(25)=0 since 2*25=50 is not the perimeter of a suitable triangle;

a(30)=2 since 2*30=60=15+20+25=10+24+26;

a(35)=1 since 2*35=70=20+21+29.

MATHEMATICA

a[n_] := Count[{x, y, z} /. {ToRules[Reduce[x>0 && y>0 && z>0 && z<y && x*y*(y+z) == n, {x, y, z}, Integers]]}, {x_, y_, z_} /; CoprimeQ[y, z] && Not[OddQ[y] && OddQ[z] || EvenQ[y] && EvenQ[z]]]; Array[a, 117] (* Jean-Fran├žois Alcover, Jun 03 2017 *)

PROG

(PARI) A270417(n) = { my(s=0); fordiv(n, x, fordiv(n/x, y, my(w=n/(x*y)); if((w < 2*y)&&(w>y)&&(w%2)&&(1==gcd(w, y)), s++))); (s); }; \\ (Here z = w-y) - Antti Karttunen, Sep 25 2018

CROSSREFS

Cf. A010814. Nonzero for terms in A005279.

Sequence in context: A291203 A256852 A128616 * A307666 A319995 A266344

Adjacent sequences:  A270414 A270415 A270416 * A270418 A270419 A270420

KEYWORD

nonn

AUTHOR

Henry Bottomley, Mar 16 2016

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 20 01:17 EDT 2019. Contains 325168 sequences. (Running on oeis4.)