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

Author

Labos Elemer, Apr 26 2002

Keywords

• nonn

Comments

Euler phi value divided by Chowla function gives integer.

Examples

			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.
		

Links

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

Crossrefs

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

Union of A000040 (primes) and A070161.

Programs

Mathematica

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

Formula

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