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

2, 6497, 12317, 91610, 133787, 181427, 404471, 439097, 485237, 1410119, 2696807, 6220607, 6827369, 6954767, 9770027, 10302419, 10449347, 10887977, 11014007, 16745387, 18959111, 25883519, 27334469, 39508037, 40311149, 40551617, 42561437, 44592209, 47717471, 48912107

Offset: 1

Author

Amiram Eldar, May 01 2020

Keywords

• nonn

Comments

Are 2 and 91610 the only even terms?

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

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).

Up to a(2214) = 2001876242879 there are no further even terms nor abundant terms. - Giovanni Resta, May 01 2020

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A000203, A033879, A033880, A112645.

Programs

Mathematica

def[n_] := 2*n - DivisorSigma[1, n]; Select[Range[10^5], def[#] == def[# + 2] &]
SequencePosition[Table[2n-DivisorSigma[1,n],{n,48920000}],{x_,,x}][[;;,1]] (* Harvey P. Dale, Apr 26 2025 *)

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