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

Offset: 1

Author

Altug Alkan, Aug 12 2020

Keywords

• nonn
• more

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

Examples

			6 is a term since 6! = 12^2 + 8^3 + 2^6.
		

Links

• David A. Corneth, PARI program

Crossrefs

Cf. A267414, A273553 (subsequence).

Programs

PARI

\\ See Corneth link. David A. Corneth, Aug 13 2020

Extensions

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