cp's OEIS Frontend

A095702 Smallest "n-augmented" amicable number: the smallest positive integer k such that m = sigma(k) - k + n > k and k = sigma(m) - m + n, where sigma(k) is the sum of the divisors of k.

%I A095702 #10 Dec 24 2020 04:47:29
%S A095702 220,6160,24,180,20,6,224,2632,40,10,16,28,340,14,15,42,66,3696,208,
%T A095702 20,21,54,264,24,68,26,88,120,102,30,4030,56,33,34,35,60,110,38,280,
%U A095702 40,354,66,476,44,130,46,408,92,1276,96,51,52,354,78,55,120,57,58,852,60,170
%N A095702 Smallest "n-augmented" amicable number: the smallest positive integer k such that m = sigma(k) - k + n > k and k = sigma(m) - m + n, where sigma(k) is the sum of the divisors of k.
%H A095702 Amiram Eldar, <a href="/A095702/b095702.txt">Table of n, a(n) for n = 0..10000</a>
%e A095702 a(1)= 6160 because sigma(6160)-6160+1 == 11697, sigma(11697)-11697+1 == 6160 and 6160 is the smallest integer for which this holds.
%t A095702 a[n_] := Module[{k = n + 1, s}, While[( s = DivisorSigma[1, k] - k + n) <= k || DivisorSigma[1, s] - s + n != k, k++]; k]; Array[a, 61, 0] (* _Amiram Eldar_, Dec 24 2020 *)
%o A095702 (PARI) for(g=0,60,x=g+1;while(1,a=sigma(x)-x+g;if((a-x)*a,if(sigma(a)-a+g==x,print1(x,",");break));x+=1))
%Y A095702 Cf. A000203, A002025, A002046, A007992, A015630.
%K A095702 nonn
%O A095702 0,1
%A A095702 _Jack Brennen_, Jul 06 2004