A129087 Odd doubly abundant numbers (A125639).

11025, 34155, 38745, 39585, 41895, 75735, 85995, 99225, 118755, 131355, 135135, 193725, 208845, 218025, 237195, 241395, 241605, 245385, 255645, 271215, 272745, 275625, 276885, 279279, 306495, 307125, 323505, 342225, 347985, 364455, 377685

Offset

1,1

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Formula

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

Example

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

Maple

filter:= proc(n) local s;
   s:= numtheory:-sigma(n)-n;
   s > n and numtheory:-sigma(s)>2*s
end proc:
select(filter, [seq(i, i=3..400000, 2)]); # Robert Israel, Jun 04 2018

Mathematica

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

Prog

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

Crossrefs

Cf. A125639, A001065, A005101.

Sequence in context: A368697 A285845 A160711 * A239828 A156942 A325311

Adjacent sequences: A129084 A129085 A129086 * A129088 A129089 A129090

Keyword

easy,nonn

Author

Ant King, Apr 02 2007

Status

approved