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A362464 Array of numbers read by upward antidiagonals: leading row lists sigma(i), i >= 1 (cf. A000203); the following rows give absolute values of differences of previous row.

%I A362464 #16 May 10 2023 06:24:07
%S A362464 1,2,3,1,1,4,1,2,3,7,1,0,2,1,6,2,3,3,5,6,12,1,3,0,3,2,4,8,0,1,2,2,1,3,
%T A362464 7,15,0,0,1,1,1,2,5,2,13,1,1,1,0,1,0,2,3,5,18,0,1,0,1,1,0,0,2,1,6,12,
%U A362464 4,4,5,5,6,7,7,7,9,10,16,28,0,4,0,5,0,6,1,6,1,8,2,14,14
%N A362464 Array of numbers read by upward antidiagonals: leading row lists sigma(i), i >= 1 (cf. A000203); the following rows give absolute values of differences of previous row.
%C A362464 The leading entries in the rows form A362451, the Gilbreath transform of sigma.
%H A362464 Paolo Xausa, <a href="/A362464/b362464.txt">Table of n, a(n) for n = 1..11325</a> (antidiagonals 1..150 of the array, flattened)
%H A362464 N. J. A. Sloane, <a href="/A362451/a362451_2.txt">Maple code for Gilbreath transform and related arrays</a>
%e A362464 The array begins:
%e A362464   1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, ...
%e A362464   2, 1, 3, 1, 6, 4, 7, 2, 5, 6, 16, 14, 10, 0, 7, ...
%e A362464   1, 2, 2, 5, 2, 3, 5, 3, 1, 10, 2, 4, 10, 7, ...
%e A362464   1, 0, 3, 3, 1, 2, 2, 2, 9, 8, 2, 6, 3, ...
%e A362464   1, 3, 0, 2, 1, 0, 0, 7, 1, 6, 4, 3, ...
%e A362464   2, 3, 2, 1, 1, 0, 7, 6, 5, 2, 1, ...
%e A362464   1, 1, 1, 0, 1, 7, 1, 1, 3, 1, ...
%e A362464   ...
%e A362464 The first few antidiagonals are:
%e A362464   1
%e A362464   2, 3
%e A362464   1, 1, 4
%e A362464   1, 2, 3, 7
%e A362464   1, 0, 2, 1, 6
%e A362464   2, 3, 3, 5, 6, 12
%e A362464   1, 3, 0, 3, 2, 4, 8
%e A362464   0, 1, 2, 2, 1, 3, 7, 15
%e A362464   ...
%p A362464 See link.
%t A362464 A362464[dmax_]:=With[{d=Reverse[NestList[Abs[Differences[#]]&,DivisorSigma[1,Range[dmax]],dmax-1]]},Array[Diagonal[d,#]&,dmax,1-dmax]];A362464[20] (* Generates 20 antidiagonals *) (* _Paolo Xausa_, May 10 2023 *)
%Y A362464 Cf. A000203, A362451.
%K A362464 nonn,look,tabl
%O A362464 1,2
%A A362464 _N. J. A. Sloane_, May 09 2023