A238232 Composite numbers n such that the sum of numbers x<=n not coprime to n divides the sum of numbers y<=n coprime to n.
15, 35, 95, 119, 143, 209, 255, 287, 319, 323, 377, 527, 559, 779, 899, 923, 989, 1007, 1189, 1199, 1295, 1343, 1349, 1763, 1919, 2159, 2507, 2759, 2911, 3239, 3599, 3827, 4031, 4607, 5183, 5207, 5249, 5459, 5543, 6439, 6479, 6887, 7067, 7279, 7739, 8159, 8639
Offset: 1
Keywords
Examples
The numbers coprime to 15 are 1, 2, 4, 7, 8, 11, 13, 14 and their sum is 60. In fact 15*phi(15)/2 = 60. The sum of the numbers from 1 to 15 is 15*(15+1)/2 = 120 and therefore the sum of the numbers not coprime to 15 is 120 - 60 = 60. At the end we have that 60/60 = 1.
Links
- Paolo P. Lava, Table of n, a(n) for n = 1..1000
Programs
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Maple
with(numtheory);P:=proc(q) local i,n; for n from 2 to q do if not isprime(n) then if type(phi(n)/(n+1-phi(n)),integer) then print(n); fi; fi; od; end: P(10^6);
Comments