

A330901


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


4



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
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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



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+ksigma(k); if(j==j1, print1(k2, ", ")); j1=j2; j2=j) \\ Hugo Pfoertner, May 01 2020


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



