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

0,1

Links

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

Example

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

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 *)

Prog

(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))

Crossrefs

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

Sequence in context: A055663 A333139 A022042 * A271674 A107506 A140918

Adjacent sequences: A095699 A095700 A095701 * A095703 A095704 A095705

Keyword

nonn

Author

Jack Brennen, Jul 06 2004

Status

approved