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A281495 Least k > 1 such that k^n is a refactorable number. 2
2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 6, 13, 9, 15, 2, 17, 6, 19, 10, 21, 8, 23, 6, 5, 26, 3, 14, 29, 30, 31, 2, 33, 34, 35, 6, 37, 38, 39, 10, 9, 42, 43, 22, 15, 46, 47, 6, 7, 10, 51, 26, 53, 6, 55, 14, 57, 58, 59, 30, 61, 62, 21, 2, 65, 66, 67, 34, 69, 70, 71, 6, 73, 74, 15, 38, 77, 78, 79 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Theorem: There are infinitely many n-th power refactorable numbers for any given value of n > 1.

For proof see Alkan link.

Numbers n such that a(n) is not equal to A007947(n+1) are 13, 21, 40, 85, 121, 171, 182, 208, 312, 341, 364, 514, 562, 585, 661, 665, 781, ...

Primes p such that a(p-1) is not equal to p are 41, 313, 563, 1013, 1201, 1823, ....

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Altug Alkan, Proof of Theorem

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

EXAMPLE

a(4) = 5 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;

CROSSREFS

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

Sequence in context: A165743 A086297 A261969 * A056554 A088835 A007947

Adjacent sequences:  A281492 A281493 A281494 * A281496 A281497 A281498

KEYWORD

nonn

AUTHOR

Altug Alkan, Jan 22 2017

STATUS

approved

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Last modified November 23 21:51 EST 2020. Contains 338603 sequences. (Running on oeis4.)