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A348048 a(n) = sigma(n) / gcd(sigma(n), A003959(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e and sigma is the sum of divisors function.

%I A348048 #12 Oct 29 2021 06:25:20
%S A348048 1,1,1,7,1,1,1,5,13,1,1,7,1,1,1,31,1,13,1,7,1,1,1,5,31,1,5,7,1,1,1,7,
%T A348048 1,1,1,91,1,1,1,5,1,1,1,7,13,1,1,31,57,31,1,7,1,5,1,5,1,1,1,7,1,1,13,
%U A348048 127,1,1,1,7,1,1,1,65,1,1,31,7,1,1,1,31,121,1,1,7,1,1,1,5,1,13,1,7,1,1,1,7,1,57,13
%N A348048 a(n) = sigma(n) / gcd(sigma(n), A003959(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e and sigma is the sum of divisors function.
%C A348048 Not multiplicative. For example, a(196) = 133 != a(4) * a(49).
%H A348048 Antti Karttunen, <a href="/A348048/b348048.txt">Table of n, a(n) for n = 1..20000</a>
%H A348048 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A348048 a(n) = A000203(n) / A348047(n) = A000203(n) / gcd(A000203(n), A003959(n)).
%t A348048 f[p_, e_] := (p + 1)^e; a[1] = 1; a[n_] := (s = DivisorSigma[1, n]) / GCD[s, Times @@ f @@@ FactorInteger[n]]; Array[a, 100] (* _Amiram Eldar_, Oct 21 2021 *)
%o A348048 (PARI)
%o A348048 A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
%o A348048 A348048(n) = { my(u=sigma(n)); (u/gcd(u, A003959(n))); };
%Y A348048 Cf. A000203, A003959, A348029, A348047, A348049.
%Y A348048 Cf. also A344696.
%K A348048 nonn
%O A348048 1,4
%A A348048 _Antti Karttunen_, Oct 21 2021