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%I #14 Mar 03 2014 04:25:30
%S 0,0,2,0,1,5,0,43,5,10,0,7,127,14,17,0,1,25,167,29,28,0,1145,2,40,213,
%T 50,41,0,4,3758,20,82,321,80,58,0,20,11,3932,32,110,387,119,77,0,71,
%U 41,34,4300,88,142,457,164,100,0,1,107,55,113,4490,212,178,531,220,129,0,7,10
%N Square array A(n,k) (n>=1, k>=0) read by antidiagonals: A(n,0) = 0 and A(n,k) is the least integer > A(n,k-1) that can be expressed as a sum of the first prime numbers divided by n.
%H Vincenzo Librandi, <a href="/A193471/b193471.txt">Table of n, a(n) for n = 1..1275</a>
%e n\k 0 1 2 3 4 5 6 7
%e -----------------------------------------
%e 1 | 0 2 5 10 17 28 41 58 A007504
%e 2 | 0 1 5 14 29 50 80 119
%e 3 | 0 43 127 167 213 321 387 457 A112270
%e 4 | 0 7 25 40 82 110 142 178
%e 5 | 0 1 2 20 32 88 212 296 A112271
%e 6 | 0 1145 3758 3932 4300 4490 4684 5084
%e 7 | 0 4 11 34 113 284 441 634 A112272
%e 8 | 0 20 41 55 71 89 158 185
%p A193471_rect := proc(n,k) local j, i, L; L := NULL; j := 0;
%p while nops([L]) < k do add(ithprime(i)/n, i=1..j);
%p if type(%,integer) then L := L,% fi; j := j+1 od; L end:
%p seq(print(A193471_rect(n, 8)), n = 1..8);
%t max = 12; rect[n_, k_] := Module[{j, i, L, s}, L = {}; j = 0; While[Length[L]<k, s = Sum[Prime[i]/n, {i, 1, j}]; If[IntegerQ[s], AppendTo[L, s]]; j = j+1]; L]; a[_, 0] = 0; a[n_, k_] := rect[n, max][[k+1]]; Table[a[n-k, k], {n, 1, max} , {k, 0, n-1}] // Flatten (* _Jean-François Alcover_, Feb 25 2014, after Maple *)
%Y Cf. A193470.
%K nonn,tabl
%O 1,3
%A _Peter Luschny_, Jul 29 2011
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