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A244409 Numbers x such that it is possible to find a value k for which Sum_{j=1..x} (x mod j) = Sum_{j=1..k} j.

%I A244409 #17 Sep 29 2014 12:25:16
%S A244409 3,4,6,13,15,16,43,112,278,346,527,845,1214,1612,2189,2863,10278,
%T A244409 610410,981350,2054106,3286515,3764767,4293562,5543363,5728393,
%U A244409 20142483,66790186,67652048,72730730,137252581,198373964,338557754,406463074,687452210,911028356
%N A244409 Numbers x such that it is possible to find a value k for which Sum_{j=1..x} (x mod j) = Sum_{j=1..k} j.
%C A244409 a(38) > 2 * 10^9. - _Hiroaki Yamanouchi_, Sep 29 2014
%H A244409 Hiroaki Yamanouchi, <a href="/A244409/b244409.txt">Table of n, a(n) for n = 1..37</a>
%F A244409 A004125(x) = A000217(k).
%e A244409 If x = 6 we have 6 mod 1 + 6 mod 2 + 6 mod 3 + 6 mod 4 + 6 mod 5 + 6 mod 6 = 0 + 0 + 0 + 2 + 1 + 0 = 3 and 1 + 2 = 3 (k = 2).
%e A244409 If x = 15 we have 15 mod 1 + 15 mod 2 + ... + 15 mod 14 + 15 mod 15 = 0 + 1 + 0 + 3 + 0 + 3 + 1 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + 0 = 36 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 (k = 8).
%p A244409 with(numtheory); P:=proc(q)local a,b,c,k,n;
%p A244409 for n from 1 to q do a:=add(n mod k,k=1..n); b:=n; c:=0;
%p A244409 while c<=a do if c=a then lprint(n,b); break; else b:=b+1;
%p A244409 c:=c+(b mod n); fi; od: od; end: P(10^9);
%Y A244409 Cf. A000217, A004125.
%K A244409 nonn
%O A244409 1,1
%A A244409 _Paolo P. Lava_, Jun 27 2014
%E A244409 a(18)-a(35) from _Hiroaki Yamanouchi_, Sep 29 2014