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%I #9 Jul 10 2022 09:44:26
%S 1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,3,1,1,5,1,1,1,1,9,1,1,
%T 1,1,1,1,1,9,1,1,1,3,1,1,1,1,1,1,1,1,1,5,1,3,1,1,1,3,1,1,1,1,1,1,1,1,
%U 1,1,1,15,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,9,1,1,1,3,1,1,1,9,1,1,1,7,1,1,1,3,1
%N a(n) = A351547(n) / A351546(n).
%H Antti Karttunen, <a href="/A354997/b354997.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>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F a(n) = A351547(n) / A351546(n).
%o (PARI)
%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A351546(n) = { my(f=factor(sigma(n)),u=A003961(n)); prod(k=1,#f~,f[k,1]^((0!=(u%f[k,1]))*f[k,2])); };
%o A351547(n) = { my(s=sigma(n),f=factor(s),u=A003961(n)); s/prod(k=1,#f~,if(!(u%f[k,1]) && (f[k,2]>=valuation(u,f[k,1])), f[k,1]^f[k,2], 1)); };
%o A354997(n) = (A351547(n) / A351546(n));
%Y Cf. A000203, A003961, A351545, A351546, A351547.
%K nonn
%O 1,8
%A _Antti Karttunen_, Jul 09 2022
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