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a(n) = A292385(A122111(n)).
7

%I #8 Jul 17 2020 22:58:19

%S 0,1,2,2,4,4,8,5,5,8,16,10,32,16,10,10,64,8,128,20,20,32,256,20,8,64,

%T 11,40,512,16,1024,20,40,128,16,21,2048,256,80,40,4096,32,8192,80,22,

%U 512,16384,40,17,17,160,160,32768,16,32,80,320,1024,65536,42,131072,2048,44,41,64,64,262144,320,640,34,524288,41,1048576,4096,20

%N a(n) = A292385(A122111(n)).

%H Antti Karttunen, <a href="/A336125/b336125.txt">Table of n, a(n) for n = 1..8192</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(1) = 0, a(2) = 1, and for n > 2, a(n) = [A122111(n) == 1 (mod 4)] + 2*a(A253553(n)).

%F a(n) = A292385(A122111(n)).

%F a(n) = A253566(n) - A336120(n).

%F A000120(a(n)) = A336123(n).

%o (PARI)

%o \\ Uses also code given in A336124:

%o A253553(n) = if(n<=2,1,my(f=factor(n), k=#f~); if(f[k,2]>1,f[k,2]--,f[k,1] = precprime(f[k,1]-1)); factorback(f));

%o A336125(n) = if(n<=2,n-1,(1==A336124(n))+(2*A336125(A253553(n))));

%o (PARI)

%o 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 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));

%o A252463(n) = if(!(n%2),n/2,A064989(n));

%o A292385(n) = if(n<=2,n-1,(1==(n%4))+(2*A292385(A252463(n))));

%o A336125(n) = A292385(A122111(n));

%Y Cf. A064989, A122111, A253553, A253566, A292385, A336120, A336123, A336313.

%K nonn

%O 1,3

%A _Antti Karttunen_, Jul 17 2020