A070161 -id:A070161 - cp's OEIS frontend

A070160 Nonprime numbers k such that phi(k)/(sigma(k) - k - 1) is an integer.

4, 9, 15, 25, 35, 49, 95, 119, 121, 143, 169, 209, 287, 289, 319, 323, 361, 377, 527, 529, 559, 779, 841, 899, 903, 923, 961, 989, 1007, 1189, 1199, 1343, 1349, 1369, 1681, 1763, 1849, 1919, 2159, 2209, 2507, 2759, 2809, 2911, 3239, 3481, 3599, 3721

Offset: 1

Labos Elemer, Apr 26 2002

nonn

Euler phi value divided by Chowla function gives integer.

			In A062972, n=15: q = 8/8 = 1; n=101: q = 100/1 = 100. While integer quotient chowla(n)/phi(n) gives only 5 nonprime solutions below 20000000 (see A070037), here, the integer reciprocals, q = phi(n)/chowla(n) obtained with squared primes and with other composites. If n=p^2, q = p(p-1)/p = p-1. So for squared primes, the quotients give A006093.

Donovan Johnson, Table of n, a(n) for n = 1..10000

Cf. A000010, A001065, A000203, A020492, A068418, A062972, A055940, A070159, A070037.

Union of A000040 (primes) and A070161.

Do[s=EulerPhi[n]/(DivisorSigma[1, n]-n-1); If[IntegerQ[s], Print[n]], {n, 2, 100000}]

{k : A000010(k)/A048050(k) is an integer}.

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.

Original entry on oeis.org

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

Paolo P. Lava, Feb 21 2014

nonn

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]

			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.

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

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

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);

cp's OEIS Frontend

A070160 Nonprime numbers k such that phi(k)/(sigma(k) - k - 1) is an integer.

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