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 A281291 Numbers n such that 2*n! is not a refactorable number. 1
 2, 4, 8, 16, 256, 65536 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A019434, A033950, A052849, A281498. Sequence in context: A321532 A061581 A046251 * A346644 A164312 A068806 Adjacent sequences:  A281288 A281289 A281290 * A281292 A281293 A281294 KEYWORD nonn,more AUTHOR Altug Alkan, Jan 23 2017 STATUS approved

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Last modified August 17 00:01 EDT 2022. Contains 356180 sequences. (Running on oeis4.)