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

1,1

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

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A000203, A033879, A033880, A112645.

Sequence in context: A349512 A107021 A107022 * A285693 A112720 A129059

Adjacent sequences: A330898 A330899 A330900 * A330902 A330903 A330904

Keyword

nonn

Author

Amiram Eldar, May 01 2020

Status

approved