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A324105 a(1) = 0; for n > 1, a(n) = A000005(A156552(n)).

%I A324105 #16 Mar 15 2019 12:34:36
%S A324105 0,1,2,2,3,2,4,2,4,3,5,2,6,2,4,4,7,2,8,2,6,4,9,2,6,4,4,4,10,4,11,2,4,
%T A324105 4,6,4,12,2,8,4,13,2,14,2,4,8,15,2,8,3,8,2,16,2,9,2,8,6,17,2,18,4,4,6,
%U A324105 6,4,19,4,4,2,20,4,21,4,4,4,8,4,22,2,8,4,23,6,12,8,16,8,24,6,12,4,12,12,12,4,25,3,8,4,26,6,27,2,8
%N A324105 a(1) = 0; for n > 1, a(n) = A000005(A156552(n)).
%C A324105 If a(n) is odd, then A067029(n) = 1 (and A319710(n) = 0), but not necessarily vice versa. See also formulas in A106737.
%H A324105 Antti Karttunen, <a href="/A324105/b324105.txt">Table of n, a(n) for n = 1..4473</a>
%H A324105 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324105 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A324105 a(1) = 0; for n > 1, a(n) = A000005(A156552(n)).
%t A324105 Array[If[# == 1, 0, DivisorSigma[0, #] &@ Floor@ Total@ Flatten@ MapIndexed[#1 2^(#2 - 1) &, Flatten[Table[2^(PrimePi@ #1 - 1), {#2}] & @@@ FactorInteger@ #]]] &, 105] (* _Michael De Vlieger_, Mar 11 2019 *)
%o A324105 (PARI)
%o A324105 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 A324105 A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
%o A324105 A324105(n) = if(1==n,0,numdiv(A156552(n)));
%Y A324105 Cf. A000005, A067029, A106737, A156552, A319710, A324051.
%Y A324105 Cf. also A323243, A324104, A324119, A324117 for similarly permuted sigma, phi, omega and A001227 (number of odd divisors).
%K A324105 nonn
%O A324105 1,3
%A A324105 _Antti Karttunen_, Feb 18 2019