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Triangle read by rows: row n gives the n primes corresponding to A187825.
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%I #10 Jan 22 2013 18:20:43

%S 3,2,3,293,307,317,1373,1451,1481,1487,6947,7109,7331,7349,7411,7173,

%T 8423,8467,8681,8693,8713,6221,6269,6311,6379,6521,6529,6551,44221,

%U 48497,49307,50111,50177,50497,50527,50543,14813,14891,14957,15053,15161,15187,15227

%N Triangle read by rows: row n gives the n primes corresponding to A187825.

%e Triangle begins:

%e n = 1 and k = 3 -> [3]

%e n = 2 and k = 2 -> [2, 3]

%e n = 3 and k = 140 -> [293, 307, 317]

%e n = 4 and k = 560 -> [1373, 1451, 1481, 1487]

%e …

%e The sequence A187825 gives the values k.

%p with(numtheory):for n from 0 to 12

%p do:ii:=0:for k from 1 to 4000000 while(ii=0) do:s:=0:x:=divisors(k):n1:=nops(x):it:=0:lst:={}: for a from n1 by -1 to 1 do:s:=s+x[a]:if type(s,prime)=true then it:=it+1:lst:=lst union {s}:else fi:od: if it = n then ii:=1: print(lst) :else fi:od:od:

%t lst={};Do[lst=Union[lst,{Prime[i]}],{i,1,5000}];a[n_]:=Catch[For[k=1,True,k++,cnt=Count[Accumulate[Divisors[k]//Reverse],_?PrimeQ];If[cnt==n,Print[Intersection[Accumulate[Divisors[k]//Reverse],lst]];Throw[k]]]];Table[a[n],{n,0,10}]

%Y Cf. A187825.

%K nonn,tabl

%O 1,1

%A _Michel Lagneau_, Jan 02 2013