A088499 Doubly (3)-perfect numbers.

27, 33, 45, 57, 69, 81, 105, 117, 141, 177, 189, 225, 249, 261, 285, 321, 357, 369, 405, 429, 441, 477, 501, 537, 585, 609, 621, 645, 657, 681, 765, 789, 825, 837, 897, 909, 945, 981, 1005, 1041, 1077, 1089, 1149, 1161, 1185, 1197, 1269, 1341, 1365, 1377

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

Sequence in context: A151742 A304243 A309063 * A058902 A342844 A141550

Adjacent sequences: A088496 A088497 A088498 * A088500 A088501 A088502

Keyword

nonn

Author

John W. Layman, Nov 11 2003

Status

approved