A117793 Pentagonal numbers divisible by 5.

0, 5, 35, 70, 145, 210, 330, 425, 590, 715, 925, 1080, 1335, 1520, 1820, 2035, 2380, 2625, 3015, 3290, 3725, 4030, 4510, 4845, 5370, 5735, 6305, 6700, 7315, 7740, 8400, 8855, 9560, 10045, 10795, 11310, 12105, 12650, 13490, 14065, 14950, 15555, 16485

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 29 2006

Keywords

• easy
• nonn

Comments

Intersection of A008587 and A000326. Their indices are given by A047215. - Michel Marcus, Feb 27 2014

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000326, A008587, A047215.

Programs

Mathematica

Select[Table[PolygonalNumber[5, n], {n, 0, 100}], Divisible[#, 5] &] (* Amiram Eldar, Mar 22 2021 *)
Select[PolygonalNumber[5,Range[0,200]],Mod[#,5]==0&] (* Harvey P. Dale, Sep 08 2024 *)

PARI

isok(n) = ispolygonal(n, 5) && !(n % 5); \\ Michel Marcus, Feb 27 2014

Formula

Empirical G.f.: x^2*(5+30*x+25*x^2+15*x^3)/(1-x)^3/(1+x)^2. - Colin Barker, Feb 14 2012

a(2*n+1) = 5*n*(15*n-1)/2, a(2*n+2) = 5*(5*n+2)*(3*n+1)/2. - Robert Israel, Jun 01 2014