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A316098 Abundant numbers that differ from the next abundant number by 4.

%I A316098 #25 Mar 01 2025 03:20:30
%S A316098 20,36,56,66,80,84,96,104,108,140,156,176,192,200,204,216,224,260,272,
%T A316098 276,300,308,320,336,360,368,380,392,396,416,440,444,456,464,476,486,
%U A316098 500,516,528,540,546,560,572,576,608,612,620,636,644,650,680,696,704
%N A316098 Abundant numbers that differ from the next abundant number by 4.
%H A316098 Muniru A Asiru, <a href="/A316098/b316098.txt">Table of n, a(n) for n = 1..10000</a>
%F A316098 a(n) = A005101(A316096(n)). - _Amiram Eldar_, Mar 01 2025
%e A316098 20 is abundant, 21, 22 and 23 are deficient, 24 is abundant.
%e A316098 36 is abundant, 37, 38 and 39 are deficient, 40 is abundant.
%p A316098 with(numtheory):  A:=select(n->sigma(n)>2*n,[$1..800]): a:=seq(A[i],i in select(n->A[n+1]-A[n]=4,[$1..nops(A)-1]));
%t A316098 q[n_] := DivisorSigma[1,n] > 2 n; Select[Range[704], q[#] && q[# + 4] && ! q[# + 1] && ! q[# + 2] && ! q[# + 3] &] (* _Giovanni Resta_, Jul 01 2018 *)
%t A316098 SequencePosition[Table[If[DivisorSigma[1,n]>2n,1,0],{n,750}],{1,0,0,0,1}][[;;,1]] (* _Harvey P. Dale_, Mar 02 2023 *)
%o A316098 (GAP) A:=Filtered([1..800],n->Sigma(n)>2*n);;  a:=List(Filtered([1..Length(A)-1],i->A[i+1]-A[i]=4),j->A[j]);
%o A316098 (PARI) list(lim) = {my(k = 1, k2); for(k2 = 2, lim, if(sigma(k2, -1) > 2, if(k2 == k1 + 4, print1(k1, ", ")); k1 = k2));} \\ _Amiram Eldar_, Mar 01 2025
%Y A316098 Subsequence of A005101.
%Y A316098 Abundant numbers that differ from the next abundant number by k: A096399 (k=1), A228382 (k=3), this sequence (k=4), A306497 (k=5), A316099 (k=6).
%Y A316098 Cf. A316096.
%K A316098 nonn
%O A316098 1,1
%A A316098 _Muniru A Asiru_, Jun 25 2018