cp's OEIS Frontend

A348992 a(n) = A000265(sigma(n)) / gcd(sigma(n), A003961(n)), where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors function.

%I A348992 #14 Nov 28 2021 12:53:14
%S A348992 1,1,1,7,3,1,1,5,13,3,3,7,7,1,3,31,9,13,5,1,1,3,3,1,31,7,1,7,15,3,1,7,
%T A348992 3,9,3,91,19,5,7,5,21,1,11,7,39,3,3,31,57,31,9,49,27,1,9,5,1,15,15,1,
%U A348992 31,1,13,127,3,3,17,7,3,3,9,13,37,19,31,35,3,7,5,31,121,21,21,7,27,11,3,5,45,39,7,7,1,3
%N A348992 a(n) = A000265(sigma(n)) / gcd(sigma(n), A003961(n)), where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors function.
%C A348992 Denominator of ratio A003961(n) / A161942(n).
%H A348992 Antti Karttunen, <a href="/A348992/b348992.txt">Table of n, a(n) for n = 1..22968</a>
%H A348992 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A348992 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A348992 a(n) = A161942(n) / A342671(n) = A000265(A349162(n)).
%F A348992 a(n) = A003961(A348993(n)).
%t A348992 Array[#1/(2^IntegerExponent[#1, 2]*GCD[##]) & @@ {DivisorSigma[1, #], Times @@ Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]]} &, 94] (* _Michael De Vlieger_, Nov 11 2021 *)
%o A348992 (PARI)
%o A348992 A000265(n) = (n >> valuation(n, 2));
%o A348992 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A348992 A348992(n) = { my(s=sigma(n)); (A000265(s)/gcd(s,A003961(n))); };
%Y A348992 Odd part of A349162.
%Y A348992 Cf. A000203, A000265, A003961, A161942, A342671, A348993, A349169 (where equal to A348990).
%Y A348992 Cf. A349161 (numerators).
%K A348992 nonn,frac
%O A348992 1,4
%A A348992 _Antti Karttunen_, Nov 10 2021