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A078319 Sum of distinct prime factors of n*rad(n)+1, where rad = A007947 (squarefree kernel).

%I A078319 #17 Apr 10 2025 05:24:40
%S A078319 2,5,7,3,15,37,7,17,9,101,63,73,24,197,115,14,36,109,183,70,32,102,60,
%T A078319 34,12,677,43,134,423,70,52,18,116,102,615,38,144,22,763,401,31,358,
%U A078319 44,39,15,102,37,17,45,170,1303,55,288,18,108,162,20,678,1743,1801,1863
%N A078319 Sum of distinct prime factors of n*rad(n)+1, where rad = A007947 (squarefree kernel).
%H A078319 Reinhard Zumkeller, <a href="/A078319/b078319.txt">Table of n, a(n) for n = 1..10000</a>
%F A078319 a(n) = A008472(A078310(n)).
%t A078319 a[n_] := Plus @@ FactorInteger[1 + n*Times @@ FactorInteger[n][[;; , 1]]][[;; , 1]]; Array[a, 100] (* _Amiram Eldar_, Apr 10 2025 *)
%o A078319 (PARI) vecprod(v)=prod(i=1,#v,v[i])
%o A078319 rad(n)=vecprod(factor(n)[,1])
%o A078319 a(n)=vecsum(factor(n*rad(n)+1)[,1]) \\ _Charles R Greathouse IV_, Jul 09 2013
%o A078319 (Haskell)
%o A078319 a078319 = a008472 . a078310  -- _Reinhard Zumkeller_, Jul 23 2013
%Y A078319 Cf. A007947, A008472, A078310, A078313, A078318, A078320.
%K A078319 nonn,easy
%O A078319 1,1
%A A078319 _Reinhard Zumkeller_, Nov 23 2002