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.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Nov 10 2021

Keywords

• nonn
• frac

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..22968
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Odd part of A349162.

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

Cf. A349161 (numerators).

Programs

Mathematica

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

PARI

A000265(n) = (n >> valuation(n, 2));
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A348992(n) = { my(s=sigma(n)); (A000265(s)/gcd(s,A003961(n))); };

Formula

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

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