A324363 a(n) = numerator of Sum_{d|n} sigma(d)/pod(d) where sigma(k) = the sum of the divisors of k (A000203) and pod(k) = the product of the divisors of k (A007955).

1, 5, 7, 27, 11, 25, 15, 231, 76, 97, 23, 2185, 27, 369, 91, 3727, 35, 9049, 39, 19041, 1565, 887, 47, 48775, 306, 615, 2092, 65, 59, 63601, 63, 119327, 1259, 1042, 4143, 55891387, 75, 2595, 5243, 1278633, 83, 713689, 87, 96711, 125216, 3785, 95, 339061279

Offset

1,2

Comments

Sum_{d|n} sigma(d)/pod(d) > 1 for all n > 1.

Links

Table of n, a(n) for n=1..48.

Formula

a(p) = 2p+1 for p = primes (A000040).

Example

For n=4; Sum_{d|4} sigma(d)/pod(d) = sigma(1)/pod(1) + sigma(2)/pod(2) + sigma(4)/pod(4) = 1/1 + 3/2 + 7/8 = 27/8; a(4) = 27.

Mathematica

Array[Numerator@ DivisorSum[#, Total[#]/(Times @@ #) &@ Divisors@ # &] &, 48] (* Michael De Vlieger, Feb 24 2019 *)

Prog

(Magma) [Numerator(&+[SumOfDivisors(d) / &*[c: c in Divisors(d)]: d in Divisors(n)]): n in [1..100]]
(PARI) a(n) = numerator(sumdiv(n, d, sigma(d)/vecprod(divisors(d)))); \\ Michel Marcus, Feb 23 2019

Crossrefs

Cf. A000040, A000203, A007955, A324364 (denominators).

Sequence in context: A013626 A067701 A059240 * A166100 A135606 A051845

Adjacent sequences: A324360 A324361 A324362 * A324364 A324365 A324366

Keyword

nonn,frac

Author

Jaroslav Krizek, Feb 23 2019

Status

approved