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a(n) = numerator of Sum_{d|n} (d/sigma(d)) where sigma(k) = the sum of the divisors of k (A000203).
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%I #8 Sep 08 2022 08:46:21

%S 1,5,7,47,11,35,15,97,127,55,23,47,27,25,77,3567,35,635,39,517,105,

%T 115,47,97,491,45,1621,235,59,385,63,37063,161,175,55,5969,75,13,27,

%U 1067,83,175,87,1081,1397,235,95,3567,1247,2455,245,423,107,1621,253,291

%N a(n) = numerator of Sum_{d|n} (d/sigma(d)) where sigma(k) = the sum of the divisors of k (A000203).

%C Sum_{d|n} (d/sigma(d)) >= 1 for all n >= 1.

%F a(p) = 2p + 1 for p = odd primes.

%e Sum_{d|n} (d/sigma(d)) for n >= 1: 1, 5/3, 7/4, 47/21, 11/6, 35/12, 15/8, 97/35, 127/52, 55/18, 23/12, 47/12, 27/14, ...

%e For n=4; Sum_{d|4} (d/sigma(d)) = 1/sigma(1) + 2/sigma(2) + 4/sigma(4) = 1/1 + 2/3 + 4/7 = 47/21; a(4) = 47.

%o (Magma) [Numerator(&+[d / SumOfDivisors(d): d in Divisors(n)]): n in [1..100]]

%o (PARI) a(n) = numerator(sumdiv(n, d, d/sigma(d))); \\ _Michel Marcus_, Mar 03 2019

%Y Cf. A000203, A306650 (denominators).

%K nonn,frac

%O 1,2

%A _Jaroslav Krizek_, Mar 03 2019