A195258 Triangle read by rows: row n gives the n primes corresponding to A187825.
3, 2, 3, 293, 307, 317, 1373, 1451, 1481, 1487, 6947, 7109, 7331, 7349, 7411, 7173, 8423, 8467, 8681, 8693, 8713, 6221, 6269, 6311, 6379, 6521, 6529, 6551, 44221, 48497, 49307, 50111, 50177, 50497, 50527, 50543, 14813, 14891, 14957, 15053, 15161, 15187, 15227
Offset: 1
Examples
Triangle begins: n = 1 and k = 3 -> [3] n = 2 and k = 2 -> [2, 3] n = 3 and k = 140 -> [293, 307, 317] n = 4 and k = 560 -> [1373, 1451, 1481, 1487] … The sequence A187825 gives the values k.
Crossrefs
Cf. A187825.
Programs
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Maple
with(numtheory):for n from 0 to 12 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: -
Mathematica
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}]