A129087 - OEIS

%I #7 Jun 05 2018 04:41:51

%S 11025,34155,38745,39585,41895,75735,85995,99225,118755,131355,135135,

%T 193725,208845,218025,237195,241395,241605,245385,255645,271215,

%U 272745,275625,276885,279279,306495,307125,323505,342225,347985,364455,377685

%N Odd doubly abundant numbers (A125639).

%C This sequence contains the odd members of A125639, which (empirically) accounts for only about 0.08% of them.

%H Robert Israel, <a href="/A129087/b129087.txt">Table of n, a(n) for n = 1..1000</a>

%F Odd numbers k, such that both k and s(k) (A001065) are abundant (A005101).

%e The third odd number which is doubly abundant is 38745. Hence a(3)=38745.

%p filter:= proc(n) local s;

%p    s:= numtheory:-sigma(n)-n;

%p    s > n and numtheory:-sigma(s)>2*s

%p end proc:

%p select(filter, [seq(i,i=3..400000,2)]); # _Robert Israel_, Jun 04 2018

%t s[n_]:=DivisorSigma[1,n]-n;DoublyAbundantNumberQ[k_]:=If[s[k]>k && s[s[k]]>s[k],True,False];Select[Range[500000],OddQ[ # ] && DoublyAbundantNumberQ[ # ] & ]

%o (PARI) isok(n) = (n%2) && ((s=sigma(n)-n) > n) && (sigma(s) > 2*s); \\ _Michel Marcus_, Jun 05 2018

%Y Cf. A125639, A001065, A005101.

%K easy,nonn

%O 1,1

%A _Ant King_, Apr 02 2007