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A347382 a(n) = A252464(n) - A252464(A000593(n)).

%I A347382 #12 Jan 30 2022 09:51:07
%S A347382 0,1,0,2,0,1,1,3,-3,1,1,2,1,2,-1,4,3,-2,3,2,0,2,4,3,-7,2,-2,3,5,0,6,5,
%T A347382 0,4,-1,-1,3,4,0,3,7,1,7,3,-3,5,9,4,-4,-6,2,3,11,-1,0,4,2,6,11,1,6,7,
%U A347382 -3,6,0,1,10,5,3,0,14,0,8,4,-8,5,-1,1,15,4,-1,8,16,2,2,8,4,4,18,-2,-1,6,5,10,2,5,19
%N A347382 a(n) = A252464(n) - A252464(A000593(n)).
%H A347382 Antti Karttunen, <a href="/A347382/b347382.txt">Table of n, a(n) for n = 1..20000</a>
%F A347382 For all n >= 0, a(2^n) = n.
%t A347382 f[p_, e_] := If[p == 2, 1, NextPrime[p, -1]^e]; g[1] = 1; g[n_] := Times @@ f @@@ FactorInteger[n]; h[1] = 0; h[n_] := h[n] = If[EvenQ[n], h[n/2] + 1, h[g[n]] + 1]; a[n_] := h[n] - h[DivisorSigma[1, n/2^IntegerExponent[n, 2]]]; Array[a, 100] (* _Amiram Eldar_, Sep 19 2021 *)
%o A347382 (PARI)
%o A347382 A000593(n) = sigma(n>>valuation(n, 2));
%o A347382 A252464(n) = if(1==n,0,(bigomega(n) + A061395(n) - 1));
%o A347382 A347382(n) = (A252464(n)-A252464(A000593(n)));
%Y A347382 Cf. A000593, A001222, A061395, A252464, A347380, A347381.
%Y A347382 Cf. also A347247, A347248.
%K A347382 sign
%O A347382 1,4
%A A347382 _Antti Karttunen_, Aug 30 2021