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.

220, 6160, 24, 180, 20, 6, 224, 2632, 40, 10, 16, 28, 340, 14, 15, 42, 66, 3696, 208, 20, 21, 54, 264, 24, 68, 26, 88, 120, 102, 30, 4030, 56, 33, 34, 35, 60, 110, 38, 280, 40, 354, 66, 476, 44, 130, 46, 408, 92, 1276, 96, 51, 52, 354, 78, 55, 120, 57, 58, 852, 60, 170

Offset: 0

Author

Jack Brennen, Jul 06 2004

Keywords

• nonn

Examples

			a(1)= 6160 because sigma(6160)-6160+1 == 11697, sigma(11697)-11697+1 == 6160 and 6160 is the smallest integer for which this holds.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000203, A002025, A002046, A007992, A015630.

Programs

Mathematica

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 *)

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))