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

1,1

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)

Formula

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A005101, A091194, A096399.

Sequence in context: A151996 A208628 A205070 * A114083 A143475 A245948

Adjacent sequences: A169819 A169820 A169821 * A169823 A169824 A169825

Keyword

nonn,changed

Author

N. J. A. Sloane, May 29 2010

Extensions

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

Status

approved