A290469 - OEIS

%I #10 Aug 04 2017 03:57:04

%S 5,10,11,14,30,145,195,367,375,471,1695,2523,9807,21249,30847,437744,

%T 2075647,2346495,8341503,14223687,33452031,15085100835

%N 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).

%C Values of k for the listed terms are 3, 4, 1, 2, 3, 2, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 2.

%e For 5 the value of k is 3. Aliquot parts of 6, 7 and 8 are: [1, 2, 3], [1], [1, 2, 4]. Residues are 0 + 1 + 2 + 0 + 0 + 1 + 1 that sum up to 5.

%p with(numtheory): P:=proc(q) local a, b, j, k, n; for n from 3 to q do

%p a:=0; k:=0; while a<n do k:=k+1; b:=sort([op(divisors(n+k))]);

%p a:=a+add(n mod b[j], j=1..nops(b)-1); od;

%p if a=n then print(n); fi; od; end: P(10^9);

%Y Cf. A286873, A290468.

%K nonn,more

%O 1,1

%A _Paolo P. Lava_, Aug 03 2017

%E a(19)-a(22) from _Giovanni Resta_, Aug 04 2017