A281389 Least k > 1 such that refactorable number k is an n-th power.

2, 9, 8, 625, 7776, 117649, 128, 6561, 1000000000, 25937424601, 362797056, 23298085122481, 2541865828329, 29192926025390625, 32768, 48661191875666868481, 16926659444736, 104127350297911241532841, 10000000000000000000, 278218429446951548637196401

Offset

1,1

Links

Table of n, a(n) for n=1..20.

S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999.

Joshua Zelinsky, Tau Numbers: A Partial Proof of a Conjecture and Other Results , Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.8

Formula

a(n) = A281495(n)^n.

Example

a(4) = 625 because 625 = 5^4 is the least fourth power refactorable number that is greater than 1.

Prog

(PARI) isA033950(n) = n % numdiv(n) == 0;
a(n) = {my(k=2); while (!isA033950 (k^n), k++); k^n; }

Crossrefs

Cf. A001597, A007947, A033950, A036907, A235524, A281495.

Sequence in context: A121067 A073904 A036879 * A073927 A198358 A145427

Adjacent sequences: A281386 A281387 A281388 * A281390 A281391 A281392

Keyword

nonn

Author

Altug Alkan, Jan 21 2017

Extensions

More terms from Giovanni Resta, Jan 22 2017

Status

approved