A180935 -id:A180935 - cp's OEIS frontend

A180936 a(n) is a power of its number of divisors.

1, 2, 9, 625, 6561, 21952, 64000, 117649, 4100625, 25937424601, 23298085122481, 29192926025390625, 59604644775390625, 300283484326400961, 48661191875666868481, 104127350297911241532841

Offset: 1

David W. Wilson, Sep 26 2010

nonn

			a(5) = 6561 = 9^4 has 9 divisors.
a(12) = 29192926025390625 = 225^7 has 225 divisors.

D. W. Wilson, Table of n, a(n) for n=1..278

Cf. A000005, A180934, A180935.

A180934 Numbers m such that m^k has m divisors for some k >= 1.

Original entry on oeis.org

1, 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 28, 29, 31, 37, 40, 41, 43, 45, 47, 49, 53, 59, 61, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 153, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 225, 227

Offset: 1

David W. Wilson, Sep 26 2010

nonn

All primes p are in this sequence, since p^(p-1) has p divisors.

For all odd semiprimes s, s^2 is in this sequence, since s^((s-1)/2) has s divisors.

			11^10 has 11 divisors, so 11 is in the sequence.
225^7 has 225 divisors, so 225 is in the sequence.

David W. Wilson, Table of n, a(n) for n=1..10000

A000005(m^k) = m for some k >= 1.
A180935 gives the corresponding k.
Cf. A036878, A046315.

q[n_] := Module[{e = FactorInteger[n][[;; , 2]], k = 1}, While[n > Times @@ (k*e + 1), k++]; n == Times @@ (k*e + 1)]; q[1] = True; Select[Range[250], q] (* Amiram Eldar, Apr 09 2024 *)

cp's OEIS Frontend

A180936 a(n) is a power of its number of divisors.

Views

Author

Keywords

Examples

Links

Crossrefs