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A374941 a(n) = (sum of proper prime factors of n) + Sum_{d = proper composite factor of n} a(d).

%I A374941 #36 Aug 18 2024 11:57:03
%S A374941 0,0,0,2,0,5,0,4,3,7,0,12,0,9,8,8,0,13,0,16,10,13,0,28,5,15,6,20,0,30,
%T A374941 0,16,14,19,12,40,0,21,16,36,0,36,0,28,19,25,0,64,7,19,20,32,0,32,16,
%U A374941 44,22,31,0,90,0,33,23,32,18,48,0,40,26,42,0,112,0,39
%N A374941 a(n) = (sum of proper prime factors of n) + Sum_{d = proper composite factor of n} a(d).
%H A374941 Michael S. Branicky, <a href="/A374941/b374941.txt">Table of n, a(n) for n = 1..10000</a>
%F A374941 a(p) = 0, iff p = 1 or a prime number.
%F A374941 a(p^k) == 2^(k-2)*p for p prime, k > 1. - _Michael S. Branicky_, Aug 01 2024
%e A374941 For n=24, the tree of recurrences "a(d)" is
%e A374941          24
%e A374941   /  /  /  \  \  \
%e A374941   2  3  4  6   8  12
%e A374941        /  / \  / \  \ \ \ \
%e A374941       2  2  3  2  4  2 3 4 6
%e A374941                  /      /  / \
%e A374941                 2      2   2  3
%e A374941 a(24) = 2 + 3 + a(4) + a(6) + a(8) + a(12)
%e A374941 = 5 + 2 + 2 + 3 + 2 + a(4) + 2 + 3 + a(4) + a(6)
%e A374941 = 14 + 2 + 5 + 2 + 2 + 3
%e A374941 = 28
%o A374941 (Python)
%o A374941 from sympy import divisors, isprime
%o A374941 def a(n): return sum(di if isprime(di) else a(di) for di in divisors(n)[1:-1])
%o A374941 print([a(n) for n in range(1, 75)]) # _Michael S. Branicky_, Jul 24 2024
%Y A374941 Cf. A371075 (fixed points).
%K A374941 nonn
%O A374941 1,4
%A A374941 _Tanmaya Mohanty_, Jul 24 2024
%E A374941 More terms from _Michael S. Branicky_, Jul 24 2024