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A348989 Denominator of A332994(n) / sigma(n).

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%I A348989 #11 Jan 24 2025 08:44:05
%S A348989 1,1,1,1,1,4,1,1,1,18,1,28,1,24,24,1,1,13,1,14,32,36,1,20,1,42,1,8,1,
%T A348989 24,1,1,48,54,48,91,1,60,56,18,1,32,1,28,39,72,1,124,1,31,72,98,1,40,
%U A348989 72,120,80,90,1,168,1,96,26,1,84,48,1,42,96,144,1,65,1,114,62,140,96,56,1,62,1,126,1,224,108,132,120
%N A348989 Denominator of A332994(n) / sigma(n).
%C A348989 See comments in A348988.
%H A348989 Antti Karttunen, <a href="/A348989/b348989.txt">Table of n, a(n) for n = 1..20000</a>
%H A348989 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A348989 a(n) = A000203(n) / A348987(n) = A000203(n) / gcd(A000203(n), A332994(n)).
%t A348989 f[n_] := n/FactorInteger[n][[-1, 1]]; g[1] = 1; g[n_] := g[n] = n + g[f[n]]; a[n_] := Denominator[g[n]/DivisorSigma[1, n]]; Array[a, 100] (* _Amiram Eldar_, Nov 06 2021 *)
%o A348989 (PARI)
%o A348989 A332994(n) = if(1==n,n,n + A332994(n/vecmax(factor(n)[,1])));
%o A348989 A348989(n) = { my(s=sigma(n)); (s/gcd(s, A332994(n))); };
%Y A348989 Cf. A000203, A332994, A333784, A348987, A348988 (numerators).
%Y A348989 Cf. also A348978, A348979.
%K A348989 nonn,frac
%O A348989 1,6
%A A348989 _Antti Karttunen_, Nov 06 2021