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

%I #14 Sep 08 2022 08:46:15

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,

%T 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,

%U 50,51,52,53,54,55,56,57,58,59,61,62,63,64,65,66,67,68,69,70,71,73

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

%C Numbers n such that A265710(n) = floor(A265708(n) / A069934(n)) = floor(A265709(n) / A265710(n)) = 1.

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

%H G. C. Greubel, <a href="/A265711/b265711.txt">Table of n, a(n) for n = 1..9268</a>

%e 6 is a term because floor(Sum_{d|6} 1/sigma(d)) = floor(1/1 + 1/3 + 1/4 + 1/12) = floor(5/3) = 1.

%t Select[Range@ 73, Floor[Sum[1/DivisorSigma[1, d], {d, Divisors@ #}]] == 1 &] (* _Michael De Vlieger_, Dec 31 2015 *)

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

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

%Y Cf. A069934, A000203, A265708, A265709, A265710, A265712, A265713, A265714, A266227, A266228.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Dec 25 2015