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%I #18 Feb 06 2024 08:13:23
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,
%U 1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1
%N a(n) = floor(Sum_{d|n} 1/sigma(d)).
%C Sequence of numbers n such that floor(Sum_{d|n} 1/sigma(d)) = k for k = 1, 2, 3:
%C k = 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ... (A265711);
%C k = 2: 60, 72, 84, 90, 120, 144, 168, 180, 210, 216, 240, 252, ... (A265712);
%C k = 3: 110880, 166320, 221760, 277200, 327600, 332640, 360360, ... (A265713).
%H Antti Karttunen, <a href="/A266227/b266227.txt">Table of n, a(n) for n = 1..16384</a>
%F a(n) = floor(Sum_{d|n} 1/A000203(d)).
%F a(n) = floor(A265708(n) / A069934(n)) = floor(A265709(n) / A265710(n)).
%e For n = 6; a(6) = floor(Sum_{d|6} 1/sigma(d)) = floor(1/1 + 1/3 + 1/4 + 1/12) = floor(5/3) = 1.
%t A266227[n_] := Floor[DivisorSum[n, 1/DivisorSigma[1, #]&]];
%t Array[A266227, 100] (* _Paolo Xausa_, Feb 06 2024 *)
%o (Magma) [Floor(&+[1/SumOfDivisors(d): d in Divisors(n)]): n in [1..100]]
%o (PARI) A266227(n) = { my(s=sumdiv(n,d,1/sigma(d))); (numerator(s) \ denominator(s)); }; \\ _Antti Karttunen_, Nov 19 2017
%Y Cf. A069934, A000203, A265708, A265709, A265710, A265711, A265712, A265713, A265714, A266228.
%K nonn
%O 1,60
%A _Jaroslav Krizek_, Dec 24 2015
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