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 A263546 #12 Nov 25 2015 02:27:09
%S A263546 1,2,6,12,15,28,40,92,111,113,145,223,268,420,625,2080,2282,2996,3371,
%T A263546 19560,38032,54426,1474778,3763906,5196340,6435993,7808592,11487666,
%U A263546 16738298,28145334,53830258,57281504,77275294,135770496,164914949
%N A263546 Numbers k such that k divides the sum of the first k primes with even indices.
%C A263546 There are 15 values of a(n) < 1000 although A045345 has 4 values A045345(n) < 1000. How do these sequences compare asymptotically?
%e A263546 1 is in the sequence because prime(2) = 3 is divisible by 1.
%e A263546 2 is in the sequence because prime(2) + prime(4) = 3 + 7 = 10 is divisible by 2.
%t A263546 Select[Range@ 10000, Divisible[Sum[Prime[2 i], {i, 1, #}], #] &] (* _Michael De Vlieger_, Oct 21 2015 *)
%o A263546 (PARI) list(lim)=my(v=List(), k, s, t); forprime(p=2, ,if((t++) && t%2==0, s+=p; k++; if(s%k==0, listput(v, k)); if(k>=lim, return(Vec(v)))))
%Y A263546 Cf. A031215, A045345, A077126, A263541.
%K A263546 nonn
%O A263546 1,2
%A A263546 _Altug Alkan_, Oct 20 2015