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 A349910 #11 Dec 15 2021 21:43:46 %S A349910 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 A349910 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 A349910 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 A349910 a(n) = Sum_{d|n, d<n} A048673(d). %H A349910 Antti Karttunen, <a href="/A349910/b349910.txt">Table of n, a(n) for n = 1..20000</a> %H A349910 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a> %F A349910 a(n) = A336840(n) - A048673(n). %t A349910 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 A349910 (PARI) %o A349910 A048673(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)+1)/2; }; %o A349910 A349910(n) = sumdiv(n,d,if(d==n,0,A048673(d))); %Y A349910 Cf. A048673, A336840. %K A349910 nonn %O A349910 1,4 %A A349910 _Antti Karttunen_, Dec 10 2021