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A352167 a(n) is the sum of the prime factors of n (with multiplicity) that are less than n.

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%I A352167 #11 Feb 16 2025 08:34:03
%S A352167 0,0,0,4,0,5,0,6,6,7,0,7,0,9,8,8,0,8,0,9,10,13,0,9,10,15,9,11,0,10,0,
%T A352167 10,14,19,12,10,0,21,16,11,0,12,0,15,11,25,0,11,14,12,20,17,0,11,16,
%U A352167 13,22,31,0,12,0,33,13,12,18,16,0,21,26,14,0,12,0,39,13,23,18,18,0,13
%N A352167 a(n) is the sum of the prime factors of n (with multiplicity) that are less than n.
%H A352167 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SumofPrimeFactors.html">Sum of Prime Factors</a>
%F A352167 a(n) = 0 if n is prime, A001414(n) otherwise.
%F A352167 a(n) = A001414(n) - A061397(n).
%t A352167 a[n_] := If[n == 1 || PrimeQ[n], 0, Plus @@ Times @@@ FactorInteger@n]; Table[a[n], {n, 80}]
%o A352167 (PARI) a(n) = if (isprime(n), 0, my(f=factor(n)); sum(k=1, #f~, f[k,1]*f[k,2])); \\ _Michel Marcus_, Mar 07 2022
%Y A352167 Cf. A001414, A061397, A105221, A144494.
%K A352167 nonn
%O A352167 1,4
%A A352167 _Ilya Gutkovskiy_, Mar 06 2022