A330901 - OEIS

%I #15 May 01 2020 12:15:34

%S 2,6497,12317,91610,133787,181427,404471,439097,485237,1410119,

%T 2696807,6220607,6827369,6954767,9770027,10302419,10449347,10887977,

%U 11014007,16745387,18959111,25883519,27334469,39508037,40311149,40551617,42561437,44592209,47717471,48912107

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

%C Are 2 and 91610 the only even terms?

%C Are there any abundant numbers (A005101) in this sequence?

%C 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 Up to a(2214) = 2001876242879 there are no further even terms nor abundant terms. - _Giovanni Resta_, May 01 2020

%H Amiram Eldar, <a href="/A330901/b330901.txt">Table of n, a(n) for n = 1..500</a>

%e 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 def[n_] := 2*n - DivisorSigma[1, n]; Select[Range[10^5], def[#] == def[# + 2] &]

%o (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 Cf. A000203, A033879, A033880, A112645.

%K nonn

%O 1,1

%A _Amiram Eldar_, May 01 2020