A321156
Numbers that have exactly 5 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
561, 1485, 1701, 2016, 2556, 2601, 2850, 3025, 3060, 3256, 3321, 4186, 4761, 4851, 5226, 5320, 5565, 5841, 6175, 6216, 6336, 6525, 6670, 7425, 7821, 7840, 8001, 8100, 8625, 8646, 9730, 9856, 9945, 9976, 10116, 10296, 10450, 10585, 11025, 11305, 11340, 12025, 12090
Offset: 1
561 has representations P(3, 188)=P(6, 39)=P(11, 12)=P(17, 6)=P(33, 3).
1485 has representations P(3, 496)=P(5, 150)=P(9, 43)=P(15, 16)=P(54, 3).
1701 has representations P(3, 568)=P(6, 115)=P(9, 49)=P(18, 13)=P(21, 10).
Cf.
A275256,
A057145,
A063778,
A129654,
A139601,
A177029,
A195527,
A195528,
A321157,
A321158,
A321159,
A321160,
A320943.
-
isok(n) = sum(k=3, n-1, ispolygonal(n, k)) == 5; \\ Michel Marcus, Oct 29 2018
-
is(n) = my(d=divisors(n<<1)); sum(i=2, #d, k=2*(d[i]^2 - 2 * d[i] + n) / (d[i] - 1) / d[i]; k == k\1 && min(d[i], k) >=3) == 5 \\ David A. Corneth, Oct 29 2018
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.
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.
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