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Numbers n such that floor(Sum_{d|n} 1 / sigma(d)) = 2.
9

%I #18 Sep 08 2022 08:46:15

%S 60,72,84,90,120,144,168,180,210,216,240,252,264,270,280,288,300,312,

%T 324,330,336,360,378,384,390,396,408,420,432,450,456,462,468,480,504,

%U 510,528,540,546,552,560,570,576,588,600,612,624,630,648,660,672,684,690

%N Numbers n such that floor(Sum_{d|n} 1 / sigma(d)) = 2.

%C Numbers n such that A265710(n) = floor(A265708(n) / A069934(n)) = floor(A265709(n) / A265710(n)) = 2.

%C See A265714(n) = the smallest number k such that floor(Sum_{d|k} 1/sigma(d)) = n.

%H G. C. Greubel, <a href="/A265712/b265712.txt">Table of n, a(n) for n = 1..7334</a>

%e 60 is a term because floor(Sum_{d|60} 1/sigma(d)) = floor(155/72) = 2.

%t Select[Range@ 690, Floor[Sum[1/DivisorSigma[1, d], {d, Divisors@ #}]] == 2 &] (* _Michael De Vlieger_, Dec 31 2015 *)

%o (Magma) [n: n in [1..1000] | Floor(&+[1/SumOfDivisors(d): d in Divisors(n)]) eq 2]

%o (PARI) isok(n) = floor(sumdiv(n, d, 1/sigma(d))) == 2; \\ _Michel Marcus_, Dec 27 2015

%Y Cf. A069934, A000203, A265708, A265709, A265710, A265711, A265713, A265714, A266227, A266228.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Dec 25 2015