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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 1 09:13 EDT 2022. Contains 357140 sequences. (Running on oeis4.)