A169822 Numbers k such that A(k+1) = A(k) + 1, where A() = A005101() are the abundant numbers.

1432, 1487, 1849, 2742, 5380, 5434, 6474, 6786, 9752, 10674, 12311, 14115, 14557, 15237, 17266, 17558, 18987, 19138, 19761, 20110, 20259, 20343, 20967, 20997, 22262, 22735, 24342, 25650, 26003, 26471, 27122, 27721, 28914, 28968, 29741, 30203, 30294, 31274, 33322

Offset: 1

Author

N. J. A. Sloane, May 29 2010

Keywords

• nonn

Comments

A096399 is the main entry for this sequence.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..7000 from Muniru A Asiru)

Crossrefs

Cf. A005101, A091194, A096399.

Programs

GAP

A:=Filtered([1..150000],n->Sigma(n)>2*n);;
  a:=Filtered([1..Length(A)-1],i->A[i+1]=A[i]+1); # Muniru A Asiru, Jun 10 2018

Maple

with(numtheory): A:=select(n->sigma(n)>2*n,[$1..150000]):
  a:=select(j->A[j+1]=A[j]+1,[$1..nops(A)-1]); # Muniru A Asiru, Jun 10 2018

Mathematica

fQ[n_] := DivisorSigma[1, n] > 2 n; lst = {}; c = 0; k = 1; While[k < 125000, If[fQ@k, c++; If[fQ[k - 1], AppendTo[lst, c - 1]]]; k++ ]; lst (* Robert G. Wilson v, Jun 11 2010 *)

PARI

list(lim) = {my(k = 1, k2, m = 0); for(k2 = 2, lim, if(sigma(k2, -1) > 2, if(k2 == k1 + 1, print1(m, ", ")); m++; k1 = k2));} \\ Amiram Eldar, Mar 01 2025

Formula

a(n) = A091194(A096399(n)). - Amiram Eldar, Mar 01 2025

Extensions

a(10) onwards from Robert G. Wilson v, Jun 11 2010