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 A165239 #19 Jul 22 2025 07:20:25
%S A165239 1,8,9,46,172,1188,4708,28611,480644,785709,1061769,24947740,31585866,
%T A165239 110275647,149612794,159273153,396643326,586740520,622899752,
%U A165239 769642427,979286966,2603393493,4102885015,4313575355,5075807081,5890950206,16152068952,62853548947
%N A165239 Integers of the form "partial sum of the first k nonprimes divided by the k-th nonprime.".
%C A165239 Integers of the form A051349(k)/A018252(k), generated by k = 1, 14, 16, 88, 334, 2345, 9328, ... - _R. J. Mathar_, Oct 29 2011
%e A165239 (1 + 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 21 + 22)/22 = 8.
%e A165239 (1 + 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 21 + 22 + 24 + 25)/25 = 9.
%e A165239 (1 + 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 21 + 22 + 24 + 25 + 26 + 27 + 28 + 30 + 32 + 33 + 34 + 35 + 36 + 38 + 39 + 40 + 42 + 44 + 45 + 46 + 48 + 49 + 50 + 51 + 52 + 54 + 55 + 56 + 57 + 58 + 60 + 62 + 63 + 64 + 65 + 66 + 68 + 69 + 70 + 72 + 74 + 75 + 76 + 77 + 78 + 80 + 81 + 82 + 84 + 85 + 86 + 87 + 88 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 98 + 99 + 100 + 102 + 104 + 105 + 106 + 108 + 110 + 111 + 112 + 114 + 115 + 116 + 117 + 118)/118 = 46.
%t A165239 lst={};a=0;Do[If[ !PrimeQ[n],m=n;a+=m;If[IntegerQ[a/n]&&a!=n,AppendTo[lst,a/n]]],{n,5*9!}];lst
%o A165239 (PARI) lista(kmax) = {my(s = 1); print1(1, ", "); forcomposite(k = 1, kmax, s += k; if(!(s%k), print1(s/k, ", ")));} \\ _Amiram Eldar_, May 24 2024
%Y A165239 Cf. A051349, A160758, A018252.
%K A165239 nonn
%O A165239 1,2
%A A165239 _Vladimir Joseph Stephan Orlovsky_, Sep 09 2009
%E A165239 a(11)-a(28) from _Amiram Eldar_, May 24 2024