A377992 Irregular triangle giving on row n all antiderivatives of A024451(n), for n >= 2.
6, 30, 58, 210, 435, 507, 2310, 8435, 21827, 29233, 30030, 39030, 62762, 69914, 76442, 78874, 510510, 1342785, 1958673, 9699690, 28235362, 223092870, 975351895, 1527890095, 1885679383, 2189118743, 2329696457, 2338611863, 3485765789, 4586671213, 5453593183, 5472849253, 5674340053, 8071055747, 8931775397, 9332889127
Offset: 2
Examples
The initial rows of the triangle: Row n terms 2 6; 3 30, 58; 4 210, 435, 507; 5 2310, 8435, 21827, 29233; 6 30030, 39030, 62762, 69914, 76442, 78874; 7 510510, 1342785, 1958673; 8 9699690, 28235362; 9 223092870, 975351895, 1527890095, ..., , 1167539981207, 1171314743479; (row 9 has 330 terms that are given separately in A378209) 10 6469693230, 27623935255, 37262208055; 11 200560490130, 345634019382, 440192669882; etc. The only terms that occur on row 4 are k = 210, 435, 507 ( = 2*3*5*7, 3*5*29, 3 * 13^2) as they are only numbers for which A003415(k) = 247 = A024451(4) = A003415(A002110(4)), as we have (2*3*5*7)' = (3*5)'*(2*7) + (2*7)'*3*5 = (8*14) + (9*15) = (3*5*29)' = (3*5)'*29 + (3*5)*29' = (8*29 + 15*1) = (3 * 13 * 13)' = (3*13)'*13 + (3*13)*13' = 16*13 + 3*13*1 = 19*13 = 247. Note that 507 is so far the only known term in this triangle that is not squarefree (in A005117).
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