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A324118 Sum of odd divisors in A156552(n): a(1) = 0, for n > 1, a(n) = A000593(A156552(n)) = A000203(A322993(n)).

%I A324118 #7 Feb 20 2019 21:43:26
%S A324118 0,1,1,4,1,6,1,8,4,13,1,12,1,18,6,24,1,14,1,20,13,48,1,24,4,84,8,48,1,
%T A324118 32,1,32,18,176,6,40,1,258,48,56,1,38,1,68,12,800,1,48,4,31,84,132,1,
%U A324118 30,13,72,176,1302,1,44,1,2736,20,104,18,96,1,304,258,42,1,72,1,4356,14,624,6,160,1,80,24,10928,1,124,48,20520,800,240,1,78,13
%N A324118 Sum of odd divisors in A156552(n): a(1) = 0, for n > 1, a(n) = A000593(A156552(n)) = A000203(A322993(n)).
%H A324118 Antti Karttunen, <a href="/A324118/b324118.txt">Table of n, a(n) for n = 1..4473</a>
%H A324118 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A324118 a(1) = 0; for n > 1, a(n) = A000593(A156552(n)) = A000203(A322993(n)) = A323243(2*A246277(n)).
%o A324118 (PARI)
%o A324118 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A324118 A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
%o A324118 A246277(n) = { if(1==n, 0, while((n%2), n = A064989(n)); (n/2)); };
%o A324118 A322993(n) = A156552(2*A246277(n));
%o A324118 A324118(n) = if(1==n, 0, sigma(A322993(n)));
%Y A324118 Cf. A000203, A000593, A156552, A246277, A322819, A322993, A323243, A324117.
%K A324118 nonn
%O A324118 1,4
%A A324118 _Antti Karttunen_, Feb 20 2019