A321160 - OEIS

%I #16 Dec 01 2018 09:12:32

%S 220780,519156,1079001,1154440,1324576,1447551,2429505,2454705,

%T 2491776,2603601,2665125,2700621,2772225,2953665,3000025,3086721,

%U 3316600,3665376,4488561,4741660,5142501,5388201,5785101,6076225

%N Numbers that have exactly 10 representations as a k-gonal number, P(n,k) = n*((k-2)*n - (k-4))/2, k and n >= 3.

%H Hugh Erling, <a href="/A321160/a321160.txt">Python program</a>

%e a(1) 220780 has representations P(n,k) = P(4, 36798) = P(7, 10515) = P(10, 4908) = P(14, 2428) = P(19, 1293) = P(28, 586) = P(35, 373) = P(38, 316) = P(40, 285) = P(664, 3).

%e a(2) 519156 has representations P(n,k) = P(3, 173053) = P(6, 34612) = P(8, 18543) = P(11, 9441) = P(27, 1481) = P(36, 826) = P(66, 244) = P(92, 126) = P(99, 109) = P(456, 7).

%e a(3) 1079001 has representations P(n,k) = P(3, 359668) = P(6, 71935) = P(9, 29974) = P(11, 19620) = P(14, 11859) = P(21, 5140) = P(27, 3076) = P(66, 505) = P(81, 335) = P(126, 139).

%o (Python) See links.

%o (PARI) isok(n) = sum(k=3, n-1, ispolygonal(n, k)) == 10; \\ _Michel Marcus_, Nov 02 2018

%Y Cf. A275256, A057145, A063778, A129654, A139601, A177029, A195527, A195528, A321156, A321157, A321158, A321159, A320943.

%K nonn

%O 1,1

%A _Hugh Erling_, Oct 29 2018