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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.
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%I #14 Nov 28 2021 12:53:14

%S 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 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 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 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 Denominator of ratio A003961(n) / A161942(n).

%H Antti Karttunen, <a href="/A348992/b348992.txt">Table of n, a(n) for n = 1..22968</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A161942(n) / A342671(n) = A000265(A349162(n)).

%F a(n) = A003961(A348993(n)).

%t Array[#1/(2^IntegerExponent[#1, 2]*GCD[##]) & @@ {DivisorSigma[1, #], Times @@ Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]]} &, 94] (* _Michael De Vlieger_, Nov 11 2021 *)

%o (PARI)

%o A000265(n) = (n >> valuation(n, 2));

%o A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A348992(n) = { my(s=sigma(n)); (A000265(s)/gcd(s,A003961(n))); };

%Y Odd part of A349162.

%Y Cf. A000203, A000265, A003961, A161942, A342671, A348993, A349169 (where equal to A348990).

%Y Cf. A349161 (numerators).

%K nonn,frac

%O 1,4

%A _Antti Karttunen_, Nov 10 2021