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).

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

Paolo P. Lava, Table of n, a(n) for n = 1..500

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

Cf. A286873, A290469.

Sequence in context: A043700 A111634 A065877 * A129917 A102577 A320427

Adjacent sequences: A290465 A290466 A290467 * A290469 A290470 A290471

Keyword

nonn

Author

Paolo P. Lava, Aug 03 2017

Status

approved