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A337046
Integers n such that n! = x^2 + y^3 + z^6 where x, y and z are nonnegative integers, is soluble.
2
0, 1, 2, 3, 4, 6, 8, 10, 14, 16, 17, 19, 20, 21, 22, 23, 24, 25
OFFSET
1,3
COMMENTS
Conjecture I: Natural density of this sequence is 1.
Conjecture II: Any sufficiently large n is in the sequence.
Conjecture III: There is a fixed value of t such that all integers >= t are terms.
If k is of the form x^2 + y^3 + z^6 then so is k*m^6 = (x*m^3)^2 + (y*m^2)^3 + (z*m)^6. - David A. Corneth, Aug 13 2020
EXAMPLE
6 is a term since 6! = 12^2 + 8^3 + 2^6.
PROG
(PARI) \\ See Corneth link. David A. Corneth, Aug 13 2020
CROSSREFS
Cf. A267414, A273553 (subsequence).
Sequence in context: A027589 A039851 A239100 * A341031 A243225 A220851
KEYWORD
nonn,more,changed
AUTHOR
Altug Alkan, Aug 12 2020
EXTENSIONS
a(12)-a(18) from David A. Corneth, Aug 12 2020
STATUS
approved