A101051 Numbers m such that Sum_{p prime|m} p^r(p) = m, where r(p) is the least positive primitive root of p (A001918).

2, 9, 25, 121, 132, 169, 343, 361, 841, 1369, 2809, 3481, 3721, 4489, 4913, 6889, 10201, 11449, 16371, 17161, 19321, 22201, 26569, 29791, 29929, 32041, 32761, 38809, 44521, 51529, 72361, 79507, 85849, 100489, 120409, 121801, 139129, 143641

Offset: 1

Author

Sven Simon, Nov 28 2004

Keywords

• nonn

Comments

Most terms m of the sequence have k = omega(m) = 1, only 132 and 16371 with k=3 are found. Further searches did not find any more terms with k >= 3. k has to be odd in any case, this can be easily seen by looking at the parity of the prime factors. Perhaps someone with a stronger computer can find more numbers with k>1, if there are any. [There are no other terms that are not prime powers among the first 1000 terms. - Amiram Eldar, Sep 25 2021]

Examples

			16371 = 3^2 * 17 * 107 = 3^2 + 17^3 + 107^2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001918.

Programs

Mathematica

f[p_, e_] := p^PrimitiveRoot[p]; q[n_] := Plus @@ f @@@ FactorInteger[n] == n; Select[Range[2, 10^5], q] (* Amiram Eldar, Sep 25 2021 *)

Extensions

Shorter name from Amiram Eldar, Sep 25 2021