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.

3, 4, 6, 13, 15, 16, 43, 112, 278, 346, 527, 845, 1214, 1612, 2189, 2863, 10278, 610410, 981350, 2054106, 3286515, 3764767, 4293562, 5543363, 5728393, 20142483, 66790186, 67652048, 72730730, 137252581, 198373964, 338557754, 406463074, 687452210, 911028356

Offset: 1

Author

Paolo P. Lava, Jun 27 2014

Keywords

• nonn

Comments

a(38) > 2 * 10^9. - Hiroaki Yamanouchi, Sep 29 2014

Examples

			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).
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).
		

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..37

Crossrefs

Cf. A000217, A004125.

Programs

Maple

with(numtheory); P:=proc(q)local a,b,c,k,n;
for n from 1 to q do a:=add(n mod k,k=1..n); b:=n; c:=0;
while c<=a do if c=a then lprint(n,b); break; else b:=b+1;
c:=c+(b mod n); fi; od: od; end: P(10^9);

Formula

A004125(x) = A000217(k).

Extensions

a(18)-a(35) from Hiroaki Yamanouchi, Sep 29 2014