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A290468
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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).
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3
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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
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OFFSET
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1,1
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COMMENTS
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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, ...
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LINKS
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EXAMPLE
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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.
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MAPLE
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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);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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