A068143
Triangular numbers which are products of triangular numbers larger than 1.
Original entry on oeis.org
36, 45, 210, 300, 378, 630, 780, 990, 1485, 1540, 2850, 3240, 3570, 4095, 4851, 4950, 5460, 8778, 9180, 11781, 15400, 17955, 19110, 21528, 25200, 26565, 26796, 31878, 33930, 37128, 37950, 39060, 40755, 43956, 52650, 61425, 61776, 70125, 79800, 82215, 97020
Offset: 1
210 is a term as 210 = 21*10 both triangular numbers.
300 is also a term since 300 = 3*10*10.
A188630 is a subsequence (only 2 factors allowed).
A364151
Tetrahedral numbers that are products of smaller tetrahedral numbers.
Original entry on oeis.org
1, 560, 19600, 43680, 45760, 893200, 1521520, 7207200, 29269240, 2845642800, 22778408800, 26595476600, 59777945920, 199910480000, 239526427140, 249466897680, 283345302240, 3280499995500, 20894643369600, 115333903584900, 408688050971200, 706949015272500, 4613394351142500
Offset: 1
1 is a term because 1 is a tetrahedral number and equals the empty product.
560 is a term because 560 = C(16,3) = C(5,3) * C(8,3). (C(n,k) is the binomial coefficient.)
45760 is a term because 45760 = C(66,3) = C(4,3)^2 * C(5,3) * C(13,3).
3280499995500 is a term because 3280499995500 = C(27001,3) = C(4,3) * C(15,3) * C(31,3) * C(135,3).
A374370
Square array read by antidiagonals: the n-th row lists n-gonal numbers that are products of smaller n-gonal numbers.
Original entry on oeis.org
1, 4, 1, 6, 36, 1, 8, 45, 16, 1, 9, 210, 36, 10045, 1, 10, 300, 64, 11310, 2850, 1, 12, 378, 81, 20475, 61776, 6426, 1, 14, 630, 100, 52360, 79800, 9828, 1408, 1, 15, 780, 144, 197472, 103740, 35224, 61920, 265926, 1, 16, 990, 196, 230300, 145530, 60606, 67200, 391950, 69300, 1
Offset: 2
Array begins:
n=2: 1, 4, 6, 8, 9, 10, 12, 14
n=3: 1, 36, 45, 210, 300, 378, 630, 780
n=4: 1, 16, 36, 64, 81, 100, 144, 196
n=5: 1, 10045, 11310, 20475, 52360, 197472, 230300, 341055
n=6: 1, 2850, 61776, 79800, 103740, 145530, 437580, 719400
n=7: 1, 6426, 9828, 35224, 60606, 1349460, 2077992, 3333330
n=8: 1, 1408, 61920, 67200, 276640, 297045, 870485, 1022000
n=9: 1, 265926, 391950, 1096200, 1767546, 1787500, 9909504, 28123200
n=10: 1, 69300, 1297890, 4257000, 5756400, 9140040, 9729720, 10648800
n=11: 1, 79135, 792330, 2382380, 5570565, 15361500, 22230000, 49888395
n=12: 1, 9504, 45696, 604128, 1981980, 2208465, 4798080, 13837824
A374500
Square pyramidal numbers that are products of smaller square pyramidal numbers.
Original entry on oeis.org
1, 4900, 513590, 333833500, 711410700, 1042716675, 1429018500, 26088481055, 62366724420, 5223660842400, 18289944673000
Offset: 1
1 is a term because it is a square pyramidal number and equals the empty product.
4900 is a term because it is a square pyramidal number and equals the product of the square pyramidal numbers 5, 5, 14, and 14.
513590 is a term because it is a square pyramidal number and equals the product of the square pyramidal numbers 506 and 1015.
Further examples:
333833500 = 506*650*1015,
711410700 = 5*385*369564,
1042716675 = 55*91*208335,
1429018500 = 285*650*7714,
26088481055 = 91*8555*33511,
62366724420 = 30*3311*627874,
5223660842400 = 140*12529*2978040,
18289944673000 = 56980*320988850.
A374501
Pentagonal pyramidal numbers that are products of smaller pentagonal pyramidal numbers.
Original entry on oeis.org
1, 56448, 127008, 259200, 5644800, 31840200, 42688800, 60766200, 116493300, 130662720, 193179168, 442828800, 499000500, 897544800, 917632800, 3624409800, 6914880000, 13831171200, 15410656800, 31246000128, 53936416800, 64024732800, 72945774720, 88957620000
Offset: 1
1 is a term because it is a pentagonal pyramidal number and equals the empty product.
56448 is a term because it is a pentagonal pyramidal number and equals the product of the pentagonal pyramidal numbers 196 and 288.
127008 is a term because it is a pentagonal pyramidal number and equals the product of the pentagonal pyramidal numbers 6, 6, 18, and 196.
A374502
Hexagonal pyramidal numbers that are products of smaller hexagonal pyramidal numbers.
Original entry on oeis.org
1, 4750, 1926049000, 655578709500, 9126464328696330
Offset: 1
1 is a term because it is a hexagonal pyramidal number and equals the empty product.
4750 is a term because it is a hexagonal pyramidal number and equals the product of the hexagonal pyramidal numbers 50 and 95.
1926049000 is a term because it is a hexagonal pyramidal number and equals the product of the hexagonal pyramidal numbers 9500 and 202742.
655578709500 is a term because it is a hexagonal pyramidal number and equals the product of the hexagonal pyramidal numbers 50, 31746, and 413015.
9126464328696330 is a term because it is a hexagonal pyramidal number and equals the product of the hexagonal pyramidal numbers 413015 and 22097174022.
A374499
Least n-gonal pyramidal number that can be written as a product of two or more smaller n-gonal pyramidal numbers, or 0 if no such number exists.
Original entry on oeis.org
36, 560, 4900, 56448, 4750, 58372180608, 1130220, 6252757280000
Offset: 2
For 2 <= n <= 9, the n-gonal pyramidal number a(n) can be written as a product of smaller n-gonal pyramidal numbers in the following ways:
n | a(n)
--+-------------------------------------
2 | 36 = 6*6
3 | 560 = 4*4*35 = 10*56
4 | 4900 = 5*5*14*14
5 | 56448 = 196*288
6 | 4750 = 50*95
7 | 58372180608 = 196*456*653108
8 | 1130220 = 9*70*1794
9 | 6252757280000 = 10*10*10*80*78159466
Showing 1-7 of 7 results.
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