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A354093 a(n) = sigma(A354091(n)), where A354091 is fully multiplicative prime shift which replaces the primes of the form 3k+2 by the next larger such prime, while other primes stay as they are, and sigma is the sum of divisors function.

%I A354093 #11 May 17 2022 17:50:21
%S A354093 1,6,4,31,12,24,8,156,13,72,18,124,14,48,48,781,24,78,20,372,32,108,
%T A354093 30,624,133,84,40,248,42,288,32,3906,72,144,96,403,38,120,56,1872,48,
%U A354093 192,44,558,156,180,54,3124,57,798,96,434,60,240,216,1248,80,252,72,1488,62,192,104,19531,168,432,68,744,120,576
%N A354093 a(n) = sigma(A354091(n)), where A354091 is fully multiplicative prime shift which replaces the primes of the form 3k+2 by the next larger such prime, while other primes stay as they are, and sigma is the sum of divisors function.
%H A354093 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A354093 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A354093 Multiplicative with a(p^e) = (q^(e+1)-1)/(q-1) where q = A003627(1+n) if p = A003627(n), otherwise q = p.
%F A354093 a(n) = Sum_{d|n} A354091(d).
%F A354093 For all n >= 1, A010872(a(n)) = A010872(A000203(n)) = A074941(n).
%o A354093 (PARI) A354093(n) = { my(f=factor(n)); for(k=1,#f~, if(2==(f[k,1]%3), for(i=1+primepi(f[k,1]),oo,if(2==(prime(i)%3), f[k,1]=prime(i); break)))); sigma(factorback(f)); };
%Y A354093 Inverse Möbius transform of A354091.
%Y A354093 Cf. A000203, A003627, A010872, A074941, A354095.
%Y A354093 Cf. A003973, A354089 for variants.
%K A354093 nonn,mult
%O A354093 1,2
%A A354093 _Antti Karttunen_, May 17 2022