A324891 - OEIS

%I #13 Mar 29 2019 08:02:57

%S 1,1,1,1,6,1,1,1,1,6,1,1,14,1,6,1,18,1,1,6,1,1,1,1,31,14,1,1,30,6,1,1,

%T 1,18,6,1,38,1,14,6,42,1,1,1,6,1,1,1,1,31,18,14,54,1,6,1,1,30,1,6,62,

%U 1,1,1,84,1,1,18,1,6,1,1,74,38,31,1,1,14,1,6,1,42,1,1,108,1,30,1,90,6,14,1,1,1,6,1,98,1,1,31,102,18,1,14,6

%N a(n) = sigma(A170818(n)), where A170818(n) is the part of n composed of prime factors of form 4k+1.

%H Antti Karttunen, <a href="/A324891/b324891.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 == 1 (mod 4), otherwise a(p^e) = 1.

%F a(n) = A000203(A170818(n)).

%F a(n) = A000593(n) / A324893(n).

%o (PARI) A324891(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4>1, 1, ((f[i,1]^(1+f[i,2]))-1)/(f[i,1]-1))); };

%o (PARI)

%o A170818(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4>1, 1, f[i, 1])^f[i, 2]); }; \\ From A170818

%o A324891(n) = sigma(A170818(n));

%Y Cf. A000203, A000593, A170818, A324893.

%K nonn,mult

%O 1,5

%A _Antti Karttunen_, Mar 27 2019