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
Florian Luca and Paul Thomas Young, On the number of divisors of n! and of the Fibonacci numbers
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