A374370 Square array read by antidiagonals: the n-th row lists n-gonal numbers that are products of smaller n-gonal numbers.

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

Author

Pontus von Brömssen, Jul 07 2024

Keywords

• nonn
• tabl

Comments

If there are only finitely many solutions for a certain value of n, the rest of that row is filled with 0's.

The first term in each row is 1, because 1 is an n-gonal number for every n and it equals the empty product.

Examples

			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
		

Crossrefs

Cf. A057145, A374371 (second column), A374498.

Rows: A018252 (n=2), A068143 (n=3 except first term), A062312 (n=4), A374372 (n=5), A374373 (n=6).