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 A078576 #14 Jan 21 2025 18:56:28 %S A078576 2,5,5,5,10,12,10,5,22,5,28,10,10,5,16,24,10,10,52,18,34,17,5,23,34, %T A078576 29,10,108,112,21,10,142,28,29,12,27,48,17,64,25,5,51,76,53,43,21,29, %U A078576 16,37,36,72,10,144,288,53,154,18,318,35,23,42,18,352,34,16,81,29,378,12 %N A078576 Sum of distinct prime factors of the average of n-th twin prime pair. %H A078576 Amiram Eldar, <a href="/A078576/b078576.txt">Table of n, a(n) for n = 1..10000</a> %F A078576 a(n) = A008472(A014574(n)). %e A078576 12th twin prime pair = (A001359(12), A006512(12)) = (149,151), hence A014574(12) = 150 = 2*3*5*5, therefore a(12) = 2+3+5 = 10. %t A078576 midQ[n_] := PrimeQ[n-1] && PrimeQ[n+1]; f[n_] := Plus @@ FactorInteger[n][[;;,1]]; f /@ Select[Range[3000], midQ] (* _Amiram Eldar_, Nov 03 2019 *) %t A078576 Total[FactorInteger[#][[;;,1]]]&/@Mean/@Select[Partition[Prime[Range[350]],2,1],#[[2]]-#[[1]]==2&] (* _Harvey P. Dale_, Jan 21 2025 *) %Y A078576 Cf. A008472, A014574, A078577, A078575, A078570. %K A078576 nonn %O A078576 1,1 %A A078576 _Reinhard Zumkeller_, Nov 29 2002