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

%I A374370 #13 Jul 11 2024 13:16:49
%S A374370 1,4,1,6,36,1,8,45,16,1,9,210,36,10045,1,10,300,64,11310,2850,1,12,
%T A374370 378,81,20475,61776,6426,1,14,630,100,52360,79800,9828,1408,1,15,780,
%U A374370 144,197472,103740,35224,61920,265926,1,16,990,196,230300,145530,60606,67200,391950,69300,1
%N A374370 Square array read by antidiagonals: the n-th row lists n-gonal numbers that are products of smaller n-gonal numbers.
%C A374370 If there are only finitely many solutions for a certain value of n, the rest of that row is filled with 0's.
%C A374370 The first term in each row is 1, because 1 is an n-gonal number for every n and it equals the empty product.
%e A374370 Array begins:
%e A374370    n=2: 1,      4,       6,       8,       9,       10,       12,       14
%e A374370    n=3: 1,     36,      45,     210,     300,      378,      630,      780
%e A374370    n=4: 1,     16,      36,      64,      81,      100,      144,      196
%e A374370    n=5: 1,  10045,   11310,   20475,   52360,   197472,   230300,   341055
%e A374370    n=6: 1,   2850,   61776,   79800,  103740,   145530,   437580,   719400
%e A374370    n=7: 1,   6426,    9828,   35224,   60606,  1349460,  2077992,  3333330
%e A374370    n=8: 1,   1408,   61920,   67200,  276640,   297045,   870485,  1022000
%e A374370    n=9: 1, 265926,  391950, 1096200, 1767546,  1787500,  9909504, 28123200
%e A374370   n=10: 1,  69300, 1297890, 4257000, 5756400,  9140040,  9729720, 10648800
%e A374370   n=11: 1,  79135,  792330, 2382380, 5570565, 15361500, 22230000, 49888395
%e A374370   n=12: 1,   9504,   45696,  604128, 1981980,  2208465,  4798080, 13837824
%Y A374370 Cf. A057145, A374371 (second column), A374498.
%Y A374370 Rows: A018252 (n=2), A068143 (n=3 except first term), A062312 (n=4), A374372 (n=5), A374373 (n=6).
%K A374370 nonn,tabl
%O A374370 2,2
%A A374370 _Pontus von Brömssen_, Jul 07 2024