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a(n) = A252464(n) - A252464(A000593(n)).
1

%I #12 Jan 30 2022 09:51:07

%S 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 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 -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 a(n) = A252464(n) - A252464(A000593(n)).

%H Antti Karttunen, <a href="/A347382/b347382.txt">Table of n, a(n) for n = 1..20000</a>

%F For all n >= 0, a(2^n) = n.

%t 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 (PARI)

%o A000593(n) = sigma(n>>valuation(n, 2));

%o A252464(n) = if(1==n,0,(bigomega(n) + A061395(n) - 1));

%o A347382(n) = (A252464(n)-A252464(A000593(n)));

%Y Cf. A000593, A001222, A061395, A252464, A347380, A347381.

%Y Cf. also A347247, A347248.

%K sign

%O 1,4

%A _Antti Karttunen_, Aug 30 2021