This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A093890 #10 Nov 17 2018 21:50:39
%S A093890 0,2,1,4,1,5,1,6,2,7,1,9,1,5,4,11,1,12,1,13,5,5,1,17,2,5,4,16,1,20,1,
%T A093890 18,4,6,6,24,1,5,5,24,1,24,1,18,11,5,1,30,1,15,3,18,1,30,6,30,5,7,1,
%U A093890 39,1,3,18,31,6,34,1,16,3,34,1,44,1,4,13,16,4,39,1,42,5,5,1,48,5,5,2,41,1,51,2
%N A093890 Number of primes arising as the sum of one or more divisors of n.
%C A093890 a(2^n) = pi(2^(n+1)-1).
%C A093890 Except for n=3 and n=42, it appears that the records occur at the highly abundant numbers A002093. The record values appear to be pi(sigma(n)) for n in A002093, which means that these n are members of A093891. [_T. D. Noe_, Mar 19 2010]
%H A093890 T. D. Noe, <a href="/A093890/b093890.txt">Table of n, a(n) for n = 1..10000</a>
%e A093890 a(4) = 4, the divisors of 4 are 1, 2 and 4.
%e A093890 Primes arising are 2, 3 = 1 + 2, 5 = 1 + 4 and 7 = 1 + 2 + 4.
%t A093890 Do[l = Subsets[Divisors[n]]; l = Union[Map[Plus @@ #&, l]]; Print[Length[Select[l, PrimeQ]]], {n, 100}] (* _Ryan Propper_, Jun 04 2006 *)
%t A093890 CountPrimes[n_] := Module[{d=Divisors[n],t,lim,x}, t=CoefficientList[Product[1+x^i, {i,d}], x]; lim=PrimePi[Length[t]-1]; Count[t[[1+Prime[Range[lim]]]], _?(#>0 &)]]; Table[CountPrimes[n], {n,100}] (* _T. D. Noe_, Mar 19 2010 *)
%Y A093890 Cf. A093891, A093892.
%Y A093890 Cf. A161510 (primes counted with repetition). [_T. D. Noe_, Mar 19 2010]
%K A093890 nonn
%O A093890 1,2
%A A093890 _Amarnath Murthy_, Apr 23 2004
%E A093890 Corrected and extended by _Ryan Propper_, Jun 04 2006