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A193934 Triangle read by rows: row n gives the n primes corresponding to A187822.

%I A193934 #12 Jan 22 2013 18:22:04
%S A193934 3,3,7,3,7,31,3,7,31,127,3,7,19,29,43,3,7,41,61,83,167,3,7,19,29,43,
%T A193934 151,271,3,11,17,53,163,409,1109,1439,3,61,79,103,283,1171,1459,3187,
%U A193934 4339,3,7,19,29,43,163,233,307,1039,1409,3,29,59,71,233,269,353
%N A193934 Triangle read by rows: row n gives the n primes corresponding to A187822.
%e A193934 Triangle begins:
%e A193934 n = 1 and k = 2  ->    [3]
%e A193934 n = 2 and k = 4  ->    [3, 7]
%e A193934 n = 3 and k = 16 ->   [3, 7, 31]
%e A193934 n = 4 and k = 64 ->   [3, 7, 31, 127]
%e A193934 n = 5 and k = 140 -> [3, 7, 19, 29, 43]
%e A193934 n = 6 and k = 440 -> [3, 7, 41, 61, 83, 167]
%e A193934 …
%e A193934 The sequence A187822 gives the values k.
%p A193934 with(numtheory):for n from 0 to 30
%p A193934 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 1 to n1 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 A193934 lst={2};Do[ lst=Union[lst ,{Prime[i]}],{i,1,5000}];a[n_]:=Catch[For[k=1,True,k++,cnt=Count[Accumulate[Divisors[k]],_?PrimeQ];If[cnt==n,Print[Intersection[Accumulate[Divisors[k]],lst]];Throw[k]]]];Table[a[n],{n,0,15}]
%Y A193934 Cf. A187822.
%K A193934 nonn,tabl
%O A193934 1,1
%A A193934 _Michel Lagneau_, Jan 02 2013