A321158 Numbers that have exactly 8 representations as a k-gonal number, P(m,k) = m*((k-2)*m - (k-4))/2, k and m >= 3.

11781, 61776, 75141, 133056, 152361, 156520, 176176, 179740, 188650, 210925, 241605, 266085, 292825, 298936, 338625, 342585, 354025, 358281, 360801, 365365, 371925, 391392, 395200, 400960, 417340, 419805, 424270, 438516

Offset: 1

Author

Hugh Erling, Oct 29 2018

Keywords

• nonn

Examples

			a(1) 11781 has representations P(m,k) = P(3, 3928)=P(6, 787)=P(9,329)=P(11, 216)=P(21, 58)=P(63, 8)=P(77, 6)=P(153, 3).
a(2) 61776 has representations P(m,k) = P(3, 20593)=P(6, 4120)=P(8,2208)=P(11, 1125)=P(26, 192)=P(36, 100)=P(176, 6)=P(351, 3).
a(3) 75141 has representations P(m,k) = P(3, 25048)=P(6, 5011)=P(9,2089)=P(11, 1368)=P(18, 493)=P(27, 216)=P(66, 37)=P(69, 34).
		

Links

• Hugh Erling, Python program

Crossrefs

Cf. A275256, A057145, A063778, A129654, A139601, A177029, A195527, A195528, A321156, A321157, A321159, A321160, A320943.

Programs

Mathematica

r[n_] := Module[{k}, Sum[Boole[d >= 3 && (k = 2(d^2 - 2d + n)/(d^2 - d); IntegerQ[k] && k >= 3)], {d, Divisors[2n]}]];
Select[Range[500000], r[#] == 8&] (* Jean-François Alcover, Sep 23 2019, after Andrew Howroyd *)

PARI

r(n)={sumdiv(2*n, d, if(d>=3, my(k=2*(d^2 - 2*d + n)/(d^2 - d)); !frac(k) && k>=3))}
for(n=1, 5*10^5, if(r(n)==8, print1(n, ", "))) \\ Andrew Howroyd, Nov 26 2018

Python

# See link.