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

1,1

Comments

Also numbers n such that n+1-phi(n) | phi(n).

A203966 lists the numbers n such that the sum of numbers x<=n coprime to n divides the sum of numbers y<=n not coprime to n. This is equivalent to numbers n such that phi(n) | n+1. [suggested by Giovanni Resta]

Links

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Example

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.

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);

Crossrefs

Cf. A061367, A050474, A070161, A142591, A203966.

Sequence in context: A368231 A109068 A334309 * A061367 A070161 A142591

Adjacent sequences: A238229 A238230 A238231 * A238233 A238234 A238235

Keyword

nonn

Author

Paolo P. Lava, Feb 21 2014

Status

approved