A321157
Numbers that have exactly 7 representations as a k-gonal number, P(n,k) = n*((k-2)*n - (k-4))/2, k and n >= 3.
Original entry on oeis.org
11935, 12376, 21736, 24220, 41041, 45441, 51360, 52326, 53361, 54145, 54405, 58311, 58696, 73360, 82720, 89425, 90321, 96580, 101025, 102025, 108801, 113050, 117216, 118405, 122265, 122500, 122760, 123201, 123256, 127281, 128961, 135201, 144585, 152076, 165376, 166635, 169456, 174097
Offset: 1
11935 has representations P(n,k) = P(5, 1195) = P(7, 570) = P(10, 267) = P(14, 133) = P(35, 22) = P(55, 10) = P(154, 3).
12376 has representations P(n,k) = P(4, 2064) = P(7, 591) = P(16, 105) = P(26, 40) = P(34, 24) = P(56, 10) = P(91, 5).
21736 has representations P(n,k) = P(4, 3624) = P(8, 778) = P(11, 397) = P(16, 183) = P(19, 129) = P(22, 96) = P(208, 3).
Cf.
A275256,
A057145,
A063778,
A129654,
A139601,
A177029,
A195527,
A195528,
A321156,
A321158,
A321159,
A321160,
A320943.
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.
Original entry on oeis.org
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
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).
Cf.
A275256,
A057145,
A063778,
A129654,
A139601,
A177029,
A195527,
A195528,
A321156,
A321157,
A321159,
A321160,
A320943.
-
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 *)
-
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
-
# See link.
A321159
Numbers that have exactly 9 representations as a k-gonal number, P(n,k) = n*((k-2)*n - (k-4))/2, k and n >= 3.
Original entry on oeis.org
27405, 126225, 194481, 201825, 273105, 478401, 538461, 615681, 718641, 859600, 862785, 1056160, 1187145, 1257201, 1328481, 1413126, 1439361, 1532601, 1540540, 1619541, 1625625, 1708785, 1842400, 1849926, 1890945
Offset: 1
a(1) 27405 has representations P(n,k) = P(3, 9136)=P(5, 2742)=P(9, 763)=P(14, 303)=P(18, 181)=P(27, 80)=P(35, 48)=P(63, 16)=P(105, 7).
a(2) 126225 has representations P(n,k) = P(3, 42076)=P(5, 12624)=P(9, 3508)=P(15, 1204)=P(17, 930)=P(33, 241)=P(50, 105)=P(99, 28)=P(225, 7).
a(3) 194481 has representations P(n,k) = P(3, 64828)=P(6, 12967)=P(9, 5404)=P(14, 2139)=P(18, 1273)=P(21, 928)=P(27, 556)=P(81, 62)=P(441, 4).
Cf.
A275256,
A057145,
A063778,
A129654,
A139601,
A177029,
A195527,
A195528,
A321156,
A321157,
A321158,
A321160,
A320943.
-
isok(n) = sum(k=3, n-1, ispolygonal(n, k)) == 9; \\ Michel Marcus, Nov 02 2018
-
# See Erling link.
A321160
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.
Original entry on oeis.org
220780, 519156, 1079001, 1154440, 1324576, 1447551, 2429505, 2454705, 2491776, 2603601, 2665125, 2700621, 2772225, 2953665, 3000025, 3086721, 3316600, 3665376, 4488561, 4741660, 5142501, 5388201, 5785101, 6076225
Offset: 1
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).
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).
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).
Cf.
A275256,
A057145,
A063778,
A129654,
A139601,
A177029,
A195527,
A195528,
A321156,
A321157,
A321158,
A321159,
A320943.
-
isok(n) = sum(k=3, n-1, ispolygonal(n, k)) == 10; \\ Michel Marcus, Nov 02 2018
-
# See links.
Showing 1-4 of 4 results.