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A228382 Abundant numbers that differ from the next abundant number by 3.

%I A228382 #27 Mar 01 2025 03:19:45
%S A228382 942,945,1572,1575,2202,2205,2832,2835,3462,3465,4092,4095,4722,4725,
%T A228382 5352,5355,5772,5985,6432,6435,6612,6615,6822,6825,7242,7245,7425,
%U A228382 7872,7875,8082,8085,8412,8415,8502,8505,8922,8925,9132,9135,9552,9555,9762,9765
%N A228382 Abundant numbers that differ from the next abundant number by 3.
%C A228382 Apparently these numbers come up mostly by pairs m, m+3 with m even; the odd terms being a subsequence of A005231. But this is not always the case (e.g., note the term 7425).
%C A228382 The numbers of terms not exceeding 10^k, for k = 3, 4, ..., are 2, 43, 393, 3635, 37599, 374092, 3731903, 37338208, 373256850, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00373... . - _Amiram Eldar_, May 30 2023
%H A228382 Muniru A Asiru, <a href="/A228382/b228382.txt">Table of n, a(n) for n = 1..10000</a>
%F A228382 a(n) = A005101(A316095(n)). - _Amiram Eldar_, Mar 01 2025
%e A228382 942 is abundant, 943 and 944 are deficient, 945 is abundant.
%e A228382 945 is abundant, 946 and 947 are deficient, 948 is abundant.
%p A228382 with(numtheory): select(n->sigma(n)>2*n and sigma(n+1)<2*(n+1) and sigma(n+2)<2*(n+2) and sigma(n+3)>2*(n+3),[$1..12000]); # _Muniru A Asiru_, Jun 09 2018
%t A228382 With[{abs = Select[Range[10000], DivisorSigma[-1, #] > 2 &]}, abs[[Position[Differences[abs], 3] // Flatten]]] (* _Amiram Eldar_, May 30 2023 *)
%t A228382 SequencePosition[Table[If[DivisorSigma[1,n]>2n,1,0],{n,10000}],{1,0,0,1}][[;;,1]] (* _Harvey P. Dale_, Aug 31 2024 *)
%o A228382 (PARI) isok(n) = (sigma(n)> 2*n) && (sigma(n+1)< 2*(n+1)) && (sigma(n+2) < 2*(n+2)) && (sigma(n+3) > 2*(n+3)); \\ _Michel Marcus_, Aug 21 2013
%o A228382 (GAP) a:=Filtered([1..130000],n->Sigma(n)>2*n and Sigma(n+1)<2*(n+1) and Sigma(n+2)<2*(n+2) and Sigma(n+3)>2*(n+3)); # _Muniru A Asiru_, Jun 09 2018
%Y A228382 Subsequence of A005101.
%Y A228382 Cf. A005231, A096399, A316095.
%K A228382 nonn
%O A228382 1,1
%A A228382 _Michel Marcus_, Aug 21 2013