A274422 Numbers m such that there exists a j for which m = Sum_{k=1..j} (m mod k), where k runs through the largest j primes less than m.

13, 17, 20, 23, 24, 34, 40, 82, 126, 200, 612, 1154, 1692, 2434, 2806, 3060, 3142, 4052, 4460, 4596, 5020, 5908, 6424, 7304, 7596, 8030, 8040, 9044, 11398, 12254, 12914, 13412, 13716, 16006, 16800, 18560, 22438, 23140, 24424, 24746, 25706, 28318, 29272, 30580

Offset: 1

Author

Paolo P. Lava, Jun 21 2016

Keywords

• nonn
• easy

Examples

			13 mod 11 + 13 mod 7 + 13 mod 5 + 13 mod 3 + 13 mod 2 = 2 + 6 + 3 + 1 + 1 = 13;
40 mod 37 + 40 mod 31 + 40 mod 29 + 40 mod 23 = 3 + 9 + 11 + 17 = 40.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..250
• Paolo P. Lava, First 200 terms with the number of primes j

Crossrefs

Cf. A000040, A024934, A274423, A274424.

Programs

Maple

P:=proc(q) local a,b,k,n; for n from 3 to q do a:=0; b:=prevprime(n);
while n>a do a:=a+(n mod b); if b>2 then b:=prevprime(b); else break; fi; od;
if n=a then print(n); fi; od; end: P(10^9);