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%I #11 Dec 15 2021 21:43:46
%S 0,1,1,3,1,6,1,8,4,7,1,19,1,9,8,22,1,27,1,23,10,10,1,56,5,12,17,31,1,
%T 47,1,63,11,13,11,93,1,15,13,69,1,65,1,35,39,18,1,165,7,43,14,43,1,
%U 128,12,95,16,19,1,160,1,22,51,185,14,74,1,47,19,80,1,288,1,24,51,55,14,92,1,205,80,25,1,226,15,27
%N a(n) = Sum_{d|n, d<n} A048673(d).
%H Antti Karttunen, <a href="/A349910/b349910.txt">Table of n, a(n) for n = 1..20000</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(n) = A336840(n) - A048673(n).
%t f[p_, e_] := NextPrime[p]^e; s[1] = 1; s[n_] := (1 + Times @@ f @@@ FactorInteger[n])/2; a[n_] := DivisorSum[n, s[#] &, # < n &]; Array[a, 100] (* _Amiram Eldar_, Dec 12 2021 *)
%o (PARI)
%o A048673(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)+1)/2; };
%o A349910(n) = sumdiv(n,d,if(d==n,0,A048673(d)));
%Y Cf. A048673, A336840.
%K nonn
%O 1,4
%A _Antti Karttunen_, Dec 10 2021
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