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A324982 a(n) = numerator of Sum_{d|n} (pod(d)/tau(d)) where pod(k) = the product of the divisors of k (A007955) and tau(k) = the number of the divisors of k (A000005). 1
1, 2, 5, 14, 7, 25, 9, 62, 23, 59, 13, 1819, 15, 109, 245, 3382, 19, 1987, 21, 2731, 465, 257, 25, 250747, 271, 355, 775, 22295, 31, 405385, 33, 28434, 1121, 599, 1253, 6726169, 39, 745, 1557, 642763, 43, 1556549, 45, 28657, 61031, 1085, 49, 765671783, 713 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Sum_{d|n} (pod(d)/tau(d)) > 1 for all n > 1.
LINKS
FORMULA
a(p) = p + 2 for p = odd primes.
EXAMPLE
Sum_{d|n} (pod(d)/tau(d)) for n >= 1: 1, 2, 5/2, 14/3, 7/2, 25/2, 9/2, 62/3, 23/2, 59/2, ...
For n=4; Sum_{d|4} (pod(d)/tau(d)) = pod(1)/tau(1) + pod(2)/tau(2) + pod(4)/tau(4) = 1/1 + 2/2 + 8/3 = 14/3; a(4) = 14.
MATHEMATICA
Array[Numerator@ DivisorSum[#, Apply[Times, Divisors@ #]/DivisorSigma[0, #] &] &, 49] (* Michael De Vlieger, Mar 24 2019 *)
PROG
(Magma) [Numerator(&+[&*[c: c in Divisors(d)] / NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]]
(PARI) a(n) = numerator(sumdiv(n, d, vecprod(divisors(d))/numdiv(d))); \\ Michel Marcus, Mar 23 2019
CROSSREFS
Cf. A000203, A007955, A324983 (denominators).
Sequence in context: A279253 A279958 A348881 * A289682 A151854 A146526
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Mar 22 2019
STATUS
approved

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Last modified July 13 15:08 EDT 2024. Contains 374284 sequences. (Running on oeis4.)