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

%I A169822 #23 Mar 01 2025 03:19:41
%S A169822 1432,1487,1849,2742,5380,5434,6474,6786,9752,10674,12311,14115,14557,
%T A169822 15237,17266,17558,18987,19138,19761,20110,20259,20343,20967,20997,
%U A169822 22262,22735,24342,25650,26003,26471,27122,27721,28914,28968,29741,30203,30294,31274,33322
%N A169822 Numbers k such that A(k+1) = A(k) + 1, where A() = A005101() are the abundant numbers.
%C A169822 A096399 is the main entry for this sequence.
%H A169822 Amiram Eldar, <a href="/A169822/b169822.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..7000 from Muniru A Asiru)
%F A169822 a(n) = A091194(A096399(n)). - _Amiram Eldar_, Mar 01 2025
%p A169822 with(numtheory): A:=select(n->sigma(n)>2*n,[$1..150000]):
%p A169822   a:=select(j->A[j+1]=A[j]+1,[$1..nops(A)-1]); # _Muniru A Asiru_, Jun 10 2018
%t A169822 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 *)
%o A169822 (GAP) A:=Filtered([1..150000],n->Sigma(n)>2*n);;
%o A169822   a:=Filtered([1..Length(A)-1],i->A[i+1]=A[i]+1); # _Muniru A Asiru_, Jun 10 2018
%o A169822 (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
%Y A169822 Cf. A005101, A091194, A096399.
%K A169822 nonn
%O A169822 1,1
%A A169822 _N. J. A. Sloane_, May 29 2010
%E A169822 a(10) onwards from _Robert G. Wilson v_, Jun 11 2010