%I #13 Mar 31 2019 02:34:00

%S 1,1,4,1,1,4,8,1,13,1,12,4,1,8,4,1,1,13,20,1,32,12,24,4,1,1,40,8,1,4,

%T 32,1,48,1,8,13,1,20,4,1,1,32,44,12,13,24,48,4,57,1,4,1,1,40,12,8,80,

%U 1,60,4,1,32,104,1,1,48,68,1,96,8,72,13,1,1,4,20,96,4,80,1,121,1,84,32,1,44,4,12,1,13,8,24,128,48,20,4,1,57,156,1,1,4

%N a(n) = sigma(A097706(n)), where A097706(n) is the part of n composed of prime factors of form 4k+3.

%H Antti Karttunen, <a href="/A324893/b324893.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F Multiplicative with a(p^e) = (p^(e+1) - 1)/(p-1) if p == 3 (mod 4), otherwise a(p^e) = 1.

%F a(n) = A000203(A097706(n)).

%F a(n) = A000593(n) / A324891(n).

%t Array[DivisorSigma[1, Times @@ Power @@@ Select[FactorInteger[#], Mod[#[[1]], 4] == 3 &]] &, 102] (* _Michael De Vlieger_, Mar 30 2019 *)

%o (PARI) A324893(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4<3, 1, ((f[i,1]^(1+f[i,2]))-1)/(f[i,1]-1))); };

%o (PARI)

%o A097706(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4<3, 1, f[i, 1])^f[i, 2]); };

%o A324893(n) = sigma(A097706(n));

%Y Cf. A000203, A000593, A097706, A324891.

%K nonn,mult

%O 1,3

%A _Antti Karttunen_, Mar 27 2019