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A290468
Numbers x such that x = Sum_{i=1..k} (x mod d_(x-i)) for some k, where d_(x-i) is the aliquot parts of (x-i).
3
11, 13, 14, 15, 18, 40, 60, 83, 205, 226, 234, 244, 267, 310, 321, 336, 341, 462, 543, 572, 610, 757, 766, 771, 802, 826, 919, 968, 993, 1089, 1366, 1391, 1734, 1758, 1863, 1911, 1985, 1993, 2095, 2222, 2396, 2405, 2422, 2522, 3495, 3634, 3655, 3672, 3823, 3870
OFFSET
1,1
COMMENTS
Values of k for the listed terms are 5, 7, 6, 9, 10, 7, 8, 7, 11, 11, 12, 12, 12, 13, 13, 15, 14, 17, 15, 18, 16, 20, 18, 19, 20, 20, 19, 22, 21, 23, 24, 25, 26, 29, 28, 28, 29, 30, 29, 30, 31, 29, 30, 33, 37, 36, 39, 39, 41, 41, ...
LINKS
EXAMPLE
For 11 the value of k is 5. Aliquot parts of 10, 9, 8, 7 and 6 are: [1, 2, 5], [1, 3], [1, 2, 4], [1], [1, 2, 3]. Residues are 0 + 1 + 1 + 0 + 2 + 0 + 1 + 3 + 0 + 0 + 1 + 2 that sum up to 11.
MAPLE
with(numtheory): P:=proc(q) local a, b, j, k, n; for n from 6 to q do
a:=0; k:=0; while a<n do k:=k+1; b:=sort([op(divisors(n-k))]);
a:=a+add(n mod b[j], j=1..nops(b)-1); od;
if a=n then print(n); fi; od; end: P(10^9);
CROSSREFS
Sequence in context: A043700 A111634 A065877 * A129917 A102577 A320427
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Aug 03 2017
STATUS
approved