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A088499 Doubly (3)-perfect numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A141550 A032584

Adjacent sequences:  A088496 A088497 A088498 * A088500 A088501 A088502

KEYWORD

nonn

AUTHOR

John W. Layman, Nov 11 2003

STATUS

approved

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Last modified September 30 10:18 EDT 2020. Contains 337439 sequences. (Running on oeis4.)