A364637 a(n) is the least k > 1 that can be represented as a sum of one or more distinct positive m-th powers for 1 <= m <= n.

2, 4, 9, 881, 7809, 134067, 12939267, 2029992385, 122120396036

Offset: 1

Author

David A. Corneth and Peter Munn, Jul 30 2023

Keywords

• nonn
• more
• hard

Comments

Sprague showed that for any m, all sufficiently large integers are the sum of distinct m-th powers. A001661(m) gives the largest number not of this form, so we can use A001661 to write an upper bound for the terms here.

Examples

			a(5) = 7809 as it can be written as a sum of one or more distinct positive m-th powers for 1 <= m <= 5 as follows. 1^5 + 2^5 + 6^5 = 2^4 + 6^4 + 7^4 + 8^4 = 3^3 + 5^3 + 14^3 + 17^3 = 1^2 + 8^2 + 88^2 = 7809^1 and no number less than 7809 can be written as such.
		

Links

• R. Sprague, Über Zerlegungen in n-te Potenzen mit lauter verschiedenen Grundzahlen, Math. Z. 51 (1948) 466-468.

Crossrefs

Sequences giving solutions for related problems: A001661, A030052.

Formula

For n >= 2, a(n) <= 1 + Max_{m=2..n} A001661(m).