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%I #10 May 02 2022 17:28:40
%S 1,1,1,9,1,12,1,27,16,18,1,9,1,24,24,27,1,16,1,27,32,36,1,27,36,42,32,
%T 6,1,72,1,243,48,54,48,3,1,60,56,3,1,96,1,27,8,72,1,81,64,108,72,7,1,
%U 64,72,54,80,90,1,27,1,96,64,729,84,144,1,81,96,48,1,36,1,114,72,15,96,168,1,243,256,126,1,18,108
%N Denominator of ratio A129283(n) / A003959(n), where A003959 is multiplicative with a(p^e) = (p+1)^e and A129283(n) is sum of n and its arithmetic derivative.
%H Antti Karttunen, <a href="/A348974/b348974.txt">Table of n, a(n) for n = 1..20000</a>
%F a(n) = A003959(n) / A348972(n) = A003959(n) / gcd(A003959(n), A129283(n)).
%t f1[p_, e_] := e/p; f2[p_, e_] := (p + 1)^e; a[n_] := Denominator[n*(1 + Plus @@ f1 @@@ (f = FactorInteger[n]))/Times @@ f2 @@@ f]; Array[a, 100] (* _Amiram Eldar_, Nov 06 2021 *)
%o (PARI)
%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
%o A348974(n) = { my(s=A003959(n)); (s/gcd(s,(n+A003415(n)))); };
%Y Cf. A003415, A003959, A129283, A348970, A348972, A348973 (numerators).
%Y Cf. also A343227.
%K nonn,frac
%O 1,4
%A _Antti Karttunen_, Nov 06 2021