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A354205 a(n) = sigma(A354202(n)), where A354202 is fully multiplicative with a(p) = A354200(A000720(p)).

%I A354205 #7 May 23 2022 17:45:57
%S A354205 1,6,8,31,14,48,12,156,57,84,20,248,18,72,112,781,30,342,24,434,96,
%T A354205 120,32,1248,183,108,400,372,38,672,44,3906,160,180,168,1767,42,144,
%U A354205 144,2184,54,576,48,620,798,192,60,6248,133,1098,240,558,62,2400,280,1872,192,228,68,3472,74,264,684,19531,252,960,72
%N A354205 a(n) = sigma(A354202(n)), where A354202 is fully multiplicative with a(p) = A354200(A000720(p)).
%H A354205 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A354205 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A354205 Multiplicative with a(p^e) = (q^(e+1)-1)/(q-1) where q = A354200(A000720(p)).
%F A354205 a(n) = A000203(A354202(n)).
%F A354205 a(n) = Sum_{d|n} A354202(d).
%o A354205 (PARI)
%o A354205 A354200(n) = if(1==n,5,my(p=prime(n), m=p%4); forprime(q=1+p,,if(m==(q%4),return(q))));
%o A354205 A354205(n) = { my(f=factor(n)); for(k=1,#f~,f[k,1] = A354200(primepi(f[k,1]))); sigma(factorback(f)); };
%o A354205 \\ Alternatively:
%o A354205 A354205(n) = sumdiv(n,d,A354202(d));
%Y A354205 Cf. A000203, A000290 (positions of odd terms), A000720, A354200, A354202, A354204, A354206.
%Y A354205 Cf. A003973, A354089, A354093 for variants.
%K A354205 nonn,mult
%O A354205 1,2
%A A354205 _Antti Karttunen_, May 23 2022