OFFSET
1,1
EXAMPLE
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.
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}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Michel Lagneau, Jan 02 2013
STATUS
approved