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A324364
a(n) = denominator 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, 2, 3, 8, 5, 6, 7, 64, 27, 25, 11, 432, 13, 98, 25, 1024, 17, 1944, 19, 4000, 441, 242, 23, 9216, 125, 169, 729, 14, 29, 11250, 31, 32768, 363, 289, 1225, 10077696, 37, 722, 1521, 256000, 41, 129654, 43, 21296, 30375, 1058, 47, 63700992, 343, 125000, 867
OFFSET
1,2
COMMENTS
Sum_{d|n} sigma(d)/pod(d) > 1 for all n > 1.
FORMULA
a(p) = p for p = primes (A000040).
a(n) = n for n = 6 or when n is a noncomposite (in A008578).
a(n) = 1 for n = 1, ... (no other n <= 10^5).
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) = 8.
MATHEMATICA
Array[Denominator@ DivisorSum[#, Total[#]/(Times @@ #) &@ Divisors@ # &] &, 51] (* Michael De Vlieger, Feb 24 2019 *)
PROG
(Magma) [Denominator(&+[SumOfDivisors(d) / &*[c: c in Divisors(d)]: d in Divisors(n)]): n in [1..100]]
(PARI) a(n) = denominator(sumdiv(n, d, sigma(d)/vecprod(divisors(d)))); \\ Michel Marcus, Feb 23 2019
CROSSREFS
Cf. A000040, A000203, A007955, A008578, A324363 (numerators).
Sequence in context: A110340 A183091 A308360 * A265344 A089489 A284047
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Feb 23 2019
STATUS
approved