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a(1) = 0; for n > 1, a(n) = A009194(A156552(n)).
7

%I #8 Mar 05 2019 18:19:44

%S 0,1,1,1,1,1,1,1,6,1,1,1,1,1,2,3,1,1,1,1,3,3,1,1,4,1,2,1,1,1,1,1,2,1,

%T 2,1,1,1,6,1,1,1,1,1,2,1,1,1,12,1,2,1,1,1,1,1,6,1,1,1,1,3,2,1,2,3,1,1,

%U 2,1,1,1,1,1,2,1,10,1,1,1,6,1,1,1,12,5,6,15,1,3,3,1,2,3,4,5,1,1,2,3,1,3,1,1,6

%N a(1) = 0; for n > 1, a(n) = A009194(A156552(n)).

%H Antti Karttunen, <a href="/A324396/b324396.txt">Table of n, a(n) for n = 1..4473</a>

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

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(1) = 0; for n > 1, a(n) = A009194(A156552(n)).

%F a(n) = gcd(A156552(n), A323243(n)).

%o (PARI)

%o A009194(n) = gcd(n, sigma(n));

%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 A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));

%o A324396(n) = if(1==n,0,A009194(A156552(n)));

%Y Cf. A009194, A156552, A323243, A323244, A324051, A324394, A324397, A324398.

%K nonn

%O 1,9

%A _Antti Karttunen_, Mar 05 2019