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%I #10 Dec 25 2020 19:31:23
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,5,1,1,
%T 1,3,1,1,1,3,1,1,1,1,1,1,1,5,1,1,1,1,1,3,1,3,1,1,1,3,1,1,1,3,1,1,1,1,
%U 1,1,1,5,1,1,1,1,1,1,1,5,9,1,1,3,1,1,1,3,1,3,1,1,1,1,1,3,1,1,1,3,1,1,1,3,1
%N a(n) = A336466(A122111(n)).
%H Antti Karttunen, <a href="/A339876/b339876.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(1) = 1, for n > 1, a(n) = A000265(A105560(n)-1) * a(A064989(n)).
%F a(n) = A336466(A122111(n)).
%o (PARI)
%o A000265(n) = (n>>valuation(n,2));
%o A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
%o A336466(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]-1))^f[k,2])); };
%o A339876(n) = A336466(A122111(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 A105560(n) = if(1==n,n,prime(bigomega(n)));
%o A339876(n) = if(1==n,n,A000265(A105560(n)-1) * A339876(A064989(n)));
%Y Cf. A000265, A064989, A105560, A122111, A336466.
%Y Cf. also A334107, A339877.
%K nonn
%O 1,16
%A _Antti Karttunen_, Dec 25 2020
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