A074391 - OEIS

%I #25 Sep 08 2022 08:45:07

%S 1,10,15,12,95,6,91,56,153,40,473,24,117,182,135,336,1139,90,703,380,

%T 861,946,3151,168,3725,468,1431,28,5017,570,775,992,891,2176,4865,792,

%U 2701,1406,585,280,6683,546,11051,1892,1305,6302,13207,528,4753,5800

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

%C 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 Each term a(n) is divisible by its index n. - _Michel Marcus_, Jan 13 2015

%H Robert Israel, <a href="/A074391/b074391.txt">Table of n, a(n) for n = 1..2000</a>

%F a(n) = Min{x; gcd(x, sigma(x))} = Min{x; gcd(x, A000203(x))} = n. - corrected by _Michel Marcus_, Jan 13 2015

%e n=6: a(6)=6 because gcd(6, sigma(6))=6 and a(6)=6 is the smallest.

%p f:= proc(n) local k;

%p   for k from n by n do

%p     if igcd(k, numtheory:-sigma(k))=n then return k fi

%p   od

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Feb 11 2020

%t 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 (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 (PARI) a(n) = my(k=1); while (gcd(sigma(k), k) != n, k++); k; \\ _Michel Marcus_, Jan 13 2015

%Y Cf. A000203, A017666, A073815, A050399, A009195, A009194.

%K nonn

%O 1,2

%A _Labos Elemer_, Aug 23 2002