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

1,4

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)

Formula

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

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

Mathematica

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

Prog

(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))); };

Crossrefs

Odd part of A349162.

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

Cf. A349161 (numerators).

Sequence in context: A010139 A078075 A067616 * A199377 A213806 A019856

Adjacent sequences: A348989 A348990 A348991 * A348993 A348994 A348995

Keyword

nonn,frac

Author

Antti Karttunen, Nov 10 2021

Status

approved