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%I #10 Sep 08 2022 08:46:24
%S 1,2,2,5,2,19,2,21,7,31,2,529,2,43,46,169,2,1135,2,1441,64,67,2,52513,
%T 11,79,64,2801,2,117001,2,2705,100,103,106,1122553,2,115,118,238561,2,
%U 317521,2,6865,6886,139,2,20247937,15,8251,154,9569,2,557443,166
%N a(n) = numerator of Sum_{d|n} (d/pod(d)) where pod(k) = the product of the divisors of k (A007955).
%C Sum_{d|n} (d/pod(d)) >= 1 for all n >= 1.
%C Sum_{d|n} (d/pod(d)) = 2 iff n = primes (A000040).
%F a(p) = 2 for p = primes.
%e Sum_{d|n} (d/pod(d)) for n >= 1: 1, 2, 2, 5/2, 2, 19/6, 2, 21/8, 7/3, 31/10, 2, 529/144, 2, 43/14, 46/15, 169/64, ...
%e For n=4; Sum_{d|4} (d/pod(d)) = 1/pod(1) + 2/pod(2) + 4/pod(4) = 1/1 + 2/2 + 4/8 = 5/2; a(4) = 5.
%t Table[Numerator[Sum[k/Product[j, {j, Divisors[k]}], {k, Divisors[n]}]], {n, 1, 60}] (* _G. C. Greubel_, Mar 04 2019 *)
%o (Magma) [Numerator(&+[d / &*[c: c in Divisors(d)]: d in Divisors(n)]): n in [1..100]]
%o (Sage) [sum(k/product(j for j in k.divisors()) for k in n.divisors()).numerator() for n in (1..60)] # _G. C. Greubel_, Mar 04 2019
%Y Cf. A000040, A007955, A007956 (denominators).
%K nonn,frac
%O 1,2
%A _Jaroslav Krizek_, Mar 03 2019
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