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

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, 151, 271, 3, 11, 17, 53, 163, 409, 1109, 1439, 3, 61, 79, 103, 283, 1171, 1459, 3187, 4339, 3, 7, 19, 29, 43, 163, 233, 307, 1039, 1409, 3, 29, 59, 71, 233, 269, 353

Offset: 1

Author

Michel Lagneau, Jan 02 2013

Keywords

• nonn
• tabl

Examples

			Triangle begins:
n = 1 and k = 2  ->    [3]
n = 2 and k = 4  ->    [3, 7]
n = 3 and k = 16 ->   [3, 7, 31]
n = 4 and k = 64 ->   [3, 7, 31, 127]
n = 5 and k = 140 -> [3, 7, 19, 29, 43]
n = 6 and k = 440 -> [3, 7, 41, 61, 83, 167]
…
The sequence A187822 gives the values k.
		

Crossrefs

Cf. A187822.

Programs

Maple

with(numtheory):for n from 0 to 30
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:

Mathematica

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}]