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 A085379 #15 Feb 16 2025 08:32:50
%S A085379 3,3,7,5,11,7,13,13,17,11,23,13,23,23,31,17,37,19,41,31,23,23,59,31,
%T A085379 41,37,53,29,71,31,61,47,53,47,89,37,59,53,89,41,89,43,83,73,71,47,
%U A085379 113,7,83,71,97,53,113,71,113,79,89,59,167,61,31,103,127,83,139,67
%N A085379 Greatest prime as sum of distinct divisors of n.
%H A085379 Amiram Eldar, <a href="/A085379/b085379.txt">Table of n, a(n) for n = 2..10001</a>
%H A085379 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DivisorFunction.html">Divisor Function</a>.
%F A085379 a(n) <= A070801(n) <= A000203(n).
%F A085379 a(A085380(n)) = A070801(A085380(n)).
%F A085379 a(A085381(n)) < A070801(A085381(n)).
%F A085379 a(A023194(n)) = A000203(A023194(n)) = A062700(n).
%e A085379 The divisors of n = 50 are {1,2,5,10,25,50}, the sums of distinct divisors that are prime: 2, 3 = 2+1, 5, 7 = 5+2, 11 = 10+1, 13 = 10+2+1, 17 = 10+5+2, 31 = 25+5+1, 37 = 25+10+2, 41 = 25+10+5+1, 43 = 25+10+5+2+1, 53 = 50+2+1, 61 = 50+10+1, 67 = 50+10+5+2 and 83 = 50+25+5+2+1. Therefore a(50) = 83 < 89 = A070801(50) and A085381(3) = 50.
%t A085379 a[n_] := Module[{d = Divisors[n], c, x}, c = Rest@CoefficientList[Series[Product[1 + x^d[[i]], {i, 1, Length[d]}], {x, 0, Total[d]}], x]; Max[Select[Position[c, _?(# > 0 &)] // Flatten, PrimeQ]]]; Array[a, 100, 2] (* _Amiram Eldar_, Mar 01 2024 *)
%Y A085379 Cf. A000203, A023194, A062700, A070801, A085380, A085381.
%K A085379 nonn
%O A085379 2,1
%A A085379 _Reinhard Zumkeller_, Jun 26 2003