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A382835 Array read by ascending antidiagonals: A(n,k) = (6*n + 1)*(12*n + 1)*Product_{i=0..k-2} (9*2^i*n + 1) with k >= 2.

%I A382835 #11 Apr 12 2025 12:31:25
%S A382835 1,91,1,325,1729,1,703,12025,63973,1,1225,38665,877825,4670029,1,1891,
%T A382835 89425,4214485,127284625,677154205,1,2701,172081,12966625,914543245,
%U A382835 36785256625,195697565245,1,3655,294409,31146661,3747354625,395997225085,21225093072625,112917495146365,1
%N A382835 Array read by ascending antidiagonals: A(n,k) = (6*n + 1)*(12*n + 1)*Product_{i=0..k-2} (9*2^i*n + 1) with k >= 2.
%C A382835 A(n,k) is a Carmichael number with k prime factors if n is such all k factors are prime numbers and 2*k-4 divides n (see Ribenboim).
%D A382835 Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 101.
%e A382835 The array begins as:
%e A382835      1,      1,        1,           1,              1, ...
%e A382835     91,   1729,    63973,     4670029,      677154205, ...
%e A382835    325,  12025,   877825,   127284625,    36785256625, ...
%e A382835    703,  38665,  4214485,   914543245,   395997225085, ...
%e A382835   1225,  89425, 12966625,  3747354625,  2162223618625, ...
%e A382835   1891, 172081, 31146661, 11243944621,  8106884071741, ...
%e A382835   2701, 294409, 63886753, 27662964049, 23928463902385, ...
%e A382835   ...
%t A382835 A[n_,k_]:=(6n+1)(12n+1)Product[9*2^i*n+1,{i,k-2}];Table[A[n-k,k],{n,0,9},{k,2,n}]//Flatten
%Y A382835 Cf. A000012 (n=0), A002997, A318646, A382809 (k=3), A382836 (antidiagonal sums).
%K A382835 nonn,tabl
%O A382835 0,2
%A A382835 _Stefano Spezia_, Apr 06 2025