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A330901 Numbers k such that k and k+2 have the same deficiency (A033879).

%I A330901 #17 Apr 26 2025 19:02:23
%S A330901 2,6497,12317,91610,133787,181427,404471,439097,485237,1410119,
%T A330901 2696807,6220607,6827369,6954767,9770027,10302419,10449347,10887977,
%U A330901 11014007,16745387,18959111,25883519,27334469,39508037,40311149,40551617,42561437,44592209,47717471,48912107
%N A330901 Numbers k such that k and k+2 have the same deficiency (A033879).
%C A330901 Are 2 and 91610 the only even terms?
%C A330901 Are there any abundant numbers (A005101) in this sequence?
%C A330901 Numbers k such that k and k+1 have the same deficiency are 1, 145215, and no more below 10^13 (they are a subset of A112645).
%C A330901 Up to a(2214) = 2001876242879 there are no further even terms nor abundant terms. - _Giovanni Resta_, May 01 2020
%H A330901 Amiram Eldar, <a href="/A330901/b330901.txt">Table of n, a(n) for n = 1..500</a>
%e A330901 2 is a term since 2 and 4 have the same deficiency: A033879(2) = 2*2 - sigma(2) = 4 - 3 = 1, and A033879(4) = 2*4 - sigma(4) = 8 - 7 = 1.
%t A330901 def[n_] := 2*n - DivisorSigma[1, n]; Select[Range[10^5], def[#] == def[# + 2] &]
%t A330901 SequencePosition[Table[2n-DivisorSigma[1,n],{n,48920000}],{x_,_,x_}][[;;,1]] (* _Harvey P. Dale_, Apr 26 2025 *)
%o A330901 (PARI) j1=1;j2=1;for(k=3,50000000,j=k+k-sigma(k);if(j==j1,print1(k-2,", "));j1=j2;j2=j) \\ _Hugo Pfoertner_, May 01 2020
%Y A330901 Cf. A000203, A033879, A033880, A112645.
%K A330901 nonn
%O A330901 1,1
%A A330901 _Amiram Eldar_, May 01 2020