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%I #19 Feb 09 2021 04:28:31
%S 4,8,9,12,16,20,24,25,27,32,36,44,45,48,49,50,54,56,60,63,64,68,72,75,
%T 80,81,88,92,96,98,99,100,104,108,112,116,117,121,125,128,132,135,136,
%U 144,147,150,153,160,162,164,168,169,171,175,176,180,184,188,189,192
%N Numbers k such that sigma(k) * Sum_{d|k} (1/sigma(d)) is not an integer.
%C A proper subset of A013929. - _Robert G. Wilson v_, Jul 21 2012
%H Amiram Eldar, <a href="/A069168/b069168.txt">Table of n, a(n) for n = 1..10000</a>
%t fQ[n_] := !IntegerQ[ DivisorSigma[1, n] Plus @@ (1/DivisorSigma[1, Divisors[n]])]; Select[ Range@ 200, fQ] (* _Robert G. Wilson v_, Jul 21 2012 *)
%o (PARI) isok(k) = denominator(sigma(k)*sumdiv(k, d, 1/sigma(d))) != 1; \\ _Michel Marcus_, Feb 09 2021
%Y Cf. A000203, A013929.
%K easy,nonn
%O 1,1
%A _Benoit Cloitre_, Apr 09 2002
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