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A074208 Least k > 1 such that n divides sigma(k) - k. 1

%I

%S 2,6,4,9,14,6,8,10,15,14,20,24,27,22,16,12,39,24,48,34,18,20,52,90,40,

%T 46,42,28,68,78,32,56,45,62,84,24,70,48,66,44,63,30,50,82,78,52,116,

%U 90,75,40,132,96,80,42,36,106,99,68,148,120,130,118,64,56,117,54,136,112

%N Least k > 1 such that n divides sigma(k) - k.

%H Ivan Neretin, <a href="/A074208/b074208.txt">Table of n, a(n) for n = 1..10000</a>

%F Conjecture: Sum_{k=1..n} a(k) = O(n^{2+epsilon}) for any epsilon > 0.

%F Between n = 90000 and 100000, Sum_{k=1..n} a(k)/n^2 slowly but not monotonically increases from 1.0007 to 1.0023. At n = 10^6, it's about 1.0147. - _David A. Corneth_, Oct 23 2017

%t a = ConstantArray[1, 68]; k = 1; While[Length[vac = Flatten[Position[a, 1]]] > 0, k++; a[[Intersection[Divisors[DivisorSigma[1, k] - k], vac]]] *= k]; a (* _Ivan Neretin_, May 15 2015 *)

%t lk[n_]:=Module[{k=2},While[!Divisible[DivisorSigma[1,k]-k,n],k++];k]; Array[lk,70] (* _Harvey P. Dale_, Oct 23 2017 *)

%o (PARI) a(n)=if(n<0,0,s=2; while((sigma(s)-s)%n>0,s++); s)

%o (PARI) first(n)=my(res = vector(n), todo = n - 1, k = 2); res[1] = 2; while(todo > 0, d = divisors(sigma(k) - k); for(i=2, #d, if(d[i] <= n && res[d[i]] == 0, res[d[i]] = k; todo--)); k++); res \\ _David A. Corneth_, Oct 23 2017

%Y Cf. A070982.

%K nonn,easy

%O 1,1

%A _Benoit Cloitre_, Sep 17 2002

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Last modified December 10 23:18 EST 2019. Contains 329910 sequences. (Running on oeis4.)