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%I #8 Aug 04 2018 14:20:45
%S 3,6,11,13,17,18,21,24,25,32,35,40,43,46,47,50,53,60,63,64,69,72,75,
%T 78,85,88,91,94,95,100,105,106,109,112,115,117,121,124,127,130,132,
%U 136,139,140,147,148,151,154,157,159,165,168,171,176,177,180,181,184
%N Numbers n such that A(n+1) = A(n) + 4, where A() = A005101() are the abundant numbers.
%F Sequence is { n | A005101(n+1) = A005101(n) + 4 }.
%F Sequence is { n | A125115(n) = 4 }.
%p with(numtheory): A:=select(n->sigma(n)>2*n,[$1..1000]): a:=select(j->A[j+1]=A[j]+4,[$1..nops(A)-1]);
%t Position[Map[{#1, #2 - 4} & @@ # &, Partition[Select[Range[10^3], DivisorSigma[1, #] > 2 # &], 2, 1]], _?(SameQ @@ # &)][[All, 1]] (* _Michael De Vlieger_, Jun 29 2018 *)
%o (GAP) A:=Filtered([1..1000],n->Sigma(n)>2*n);; a:=Filtered([1..Length(A)-1],i->A[i+1]=A[i]+4);
%Y A316098 is the main sequence for this entry.
%Y Numbers n such that A(n+1) = A(n) + k, where A() = A005101() are the abundant numbers: A169822 (k=1), A303741 (k=2), A316095 (k=3), this sequence (k=4), A316097 (k=6).
%Y Cf. A005101.
%K nonn
%O 1,1
%A _Muniru A Asiru_, Jun 25 2018
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