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A074391 a(n) is the smallest number such that gcd(a(n), sigma(a(n))) = n.

%I A074391 #25 Sep 08 2022 08:45:07
%S A074391 1,10,15,12,95,6,91,56,153,40,473,24,117,182,135,336,1139,90,703,380,
%T A074391 861,946,3151,168,3725,468,1431,28,5017,570,775,992,891,2176,4865,792,
%U A074391 2701,1406,585,280,6683,546,11051,1892,1305,6302,13207,528,4753,5800
%N A074391 a(n) is the smallest number such that gcd(a(n), sigma(a(n))) = n.
%C A074391 a(n) is the smallest number k such that A017666(k), the denominator of sigma(k)/k, is equal to k/n. - _Jaroslav Krizek_, Sep 23 2014
%C A074391 Each term a(n) is divisible by its index n. - _Michel Marcus_, Jan 13 2015
%H A074391 Robert Israel, <a href="/A074391/b074391.txt">Table of n, a(n) for n = 1..2000</a>
%F A074391 a(n) = Min{x; gcd(x, sigma(x))} = Min{x; gcd(x, A000203(x))} = n. - corrected by _Michel Marcus_, Jan 13 2015
%e A074391 n=6: a(6)=6 because gcd(6, sigma(6))=6 and a(6)=6 is the smallest.
%p A074391 f:= proc(n) local k;
%p A074391   for k from n by n do
%p A074391     if igcd(k, numtheory:-sigma(k))=n then return k fi
%p A074391   od
%p A074391 end proc:
%p A074391 map(f, [$1..100]); # _Robert Israel_, Feb 11 2020
%t A074391 f[x_] := GCD[DivisorSigma[1, x], x] t=Table[0, {100}]; Do[s=f[n]; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 1000000}];
%o A074391 (Magma) A074391:=func<n|exists(r){k: k in[1..1000000] | Denominator(SumOfDivisors(k)/k) eq k/n}select r else-1>; [A074391(n): n in[1..100]] // _Jaroslav Krizek_, Sep 23 2014
%o A074391 (PARI) a(n) = my(k=1); while (gcd(sigma(k), k) != n, k++); k; \\ _Michel Marcus_, Jan 13 2015
%Y A074391 Cf. A000203, A017666, A073815, A050399, A009195, A009194.
%K A074391 nonn
%O A074391 1,2
%A A074391 _Labos Elemer_, Aug 23 2002