A337046 - OEIS

A337046

Integers n such that n! = x^2 + y^3 + z^6 where x, y and z are nonnegative integers, is soluble.

0, 1, 2, 3, 4, 6, 8, 10, 14, 16, 17, 19, 20, 21, 22, 23, 24, 25

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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

LINKS

David A. Corneth, PARI program

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).

KEYWORD

nonn,more

AUTHOR

Altug Alkan, Aug 12 2020

EXTENSIONS

a(12)-a(18) from David A. Corneth, Aug 12 2020

STATUS

approved