cp's OEIS Frontend

A348986 Denominator of ratio sigma(n) / A325973(n), where A325973 is the arithmetic mean of {sum of squarefree divisors} and {sum of unitary divisors}.

%I A348986 #11 Nov 11 2021 14:44:48
%S A348986 1,1,1,4,1,1,1,2,7,1,1,4,1,1,1,10,1,7,1,4,1,1,1,2,16,1,2,4,1,1,1,2,1,
%T A348986 1,1,31,1,1,1,2,1,1,1,4,7,1,1,10,29,16,1,4,1,2,1,2,1,1,1,4,1,1,7,34,1,
%U A348986 1,1,4,1,1,1,17,1,1,16,4,1,1,1,10,43,1,1,4,1,1,1,2,1,7,1,4,1,1,1,2,1,29,7,74,1,1,1,2,1
%N A348986 Denominator of ratio sigma(n) / A325973(n), where A325973 is the arithmetic mean of {sum of squarefree divisors} and {sum of unitary divisors}.
%C A348986 This is not multiplicative: a(4) = 4 and a(9) = 7, but a(36) = 31, not 28.
%H A348986 Antti Karttunen, <a href="/A348986/b348986.txt">Table of n, a(n) for n = 1..20000</a>
%H A348986 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A348986 a(n) = A325973(n) / A348984(n) = A325973(n) / gcd(A000203(n), A325973(n)).
%t A348986 f1[p_, e_] := p + 1; f2[p_, e_] := p^e + 1; s[1] = 1; s[n_] := (Times @@ f1 @@@ (f = FactorInteger[n]) + Times @@ f2 @@@ f)/2; a[n_] := Denominator[DivisorSigma[1, n]/s[n]]; Array[a, 100] (* _Amiram Eldar_, Nov 06 2021 *)
%o A348986 (PARI)
%o A348986 A325973(n) = (1/2)*sumdiv(n, d, d*(issquarefree(d) + (1==gcd(d, n/d))));
%o A348986 A348986(n) = { my(am=A325973(n)); (am/gcd(sigma(n),am)); };
%Y A348986 Cf. A000203, A048250, A034448, A325973, A325974, A348984, A348985 (numerators).
%Y A348986 Cf. also A348947.
%K A348986 nonn,frac
%O A348986 1,4
%A A348986 _Antti Karttunen_, Nov 06 2021