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A281291
Numbers n such that 2*n! is not a refactorable number.
1
2, 4, 8, 16, 256, 65536
OFFSET
1,1
COMMENTS
See Conjecture 47 and Theorem 51 in Zelinsky's paper for related points.
In Theorem 51 Zelinsky gives a technical result which almost implies that for all sufficiently large n, n! is a refactorable number. (Corrected by Joshua Zelinsky, May 15 2020)
Also note that Luca & Young paper gives a proof for n! is a refactorable number for all n > 5.
This sequence focuses on the 2 * n! and we cannot say that 2 * n! is refactorable for all sufficiently large n at the moment. This is because if 2^(2^k) + 1 is a Fermat prime (A019434), then 2^(2^k) is a term of this sequence and it is not known yet sequence of Fermat primes is finite or not.
LINKS
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
8 is a term since d(2*8!) = 2^2 * 3^3 does not divide 2 * 8! = 2^8 * 3^2 * 5 * 7.
PROG
(PARI) isA033950(n) = n % numdiv(n) == 0;
is(n) = !isA033950(2*n!);
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Altug Alkan, Jan 23 2017
STATUS
approved