OFFSET
1,1
COMMENTS
We define a doubly (r)-perfect number n as one for which Sum[d; 1<=d<n, n mod d=r] = 2n. It appears that all differences, a(n+1)-a(n), of consecutive (3)-perfect numbers are multiples of 6.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..500
EXAMPLE
27 is a (3)-perfect number since the integers d in 1..26 for which 27 mod d=3 are 4, 6, 8, 12 and 24 and these sum to 54=2*27.
MATHEMATICA
d3pnQ[n_]:=Total[Select[Range[n-1], Mod[n, #]==3&]]==2 n; Select[Range[1400], d3pnQ] (* Harvey P. Dale, May 15 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
John W. Layman, Nov 11 2003
STATUS
approved