A225819 Consider the set of n-tuples such that the sum of cubes of the elements is equal to square of their sum; sequence gives largest element in all such tuples.
1, 2, 3, 4, 6, 7, 9, 10, 12, 14, 16, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 42, 44, 46, 48, 51, 53, 55, 58, 60, 62, 65, 67, 70, 72, 75, 77, 80, 82, 85, 88, 90, 93, 96, 98, 101, 104, 106, 109, 112, 115, 117, 120, 123, 126, 129, 132, 134, 137, 140, 143, 146, 149, 152, 155
Offset: 1
Keywords
Examples
Call an n-multiset with the sum of cubes of the elements equal to square of their sum an n-SCESS. a(6) = 7 since the only 6-SCESS with the largest element >= 7 are (2, 4, 4, 5, 5, 7), (3, 3, 3, 3, 5, 7), (3, 4, 5, 5, 6, 7), (3, 5, 5, 5, 6, 7) and (4, 5, 5, 6, 6, 7) and none have an element larger than 7. a(7) = 9 since the only 7-SCESS with the largest element >= 9 are (4, 4, 4, 5, 5, 5, 9), (4, 5, 5, 5, 6, 6, 9) and (6, 6, 6, 6, 6, 6, 9) and none have an element larger than 9. a(8) = 10 since the only 8-SCESS with the largest element >= 10 are (2, 5, 5, 5, 5, 5, 6, 10), (2, 6, 6, 6, 6, 6, 6, 10), (3, 4, 5, 5, 5, 6, 7, 10), (3, 4, 5, 5, 6, 6, 7, 10), (3, 5, 5, 5, 6, 7, 7, 10), (3, 6, 6, 6, 7, 7, 7, 10), (4, 4, 4, 4, 4, 4, 6, 10), (4, 4, 4, 4, 5, 5, 7, 10), (4, 5, 5, 6, 6, 7, 8, 10), (5, 5, 5, 7, 7, 7, 8, 10) and (6, 6, 6, 6, 6, 6, 9, 10) and none have an element larger than 10.
Links
- Balarka Sen, Table of n, a(n) for n = 1..500
- John Mason, Generalising 'sums of cubes equal to squares of sums', The Mathematical Gazette 85:502 (2001), pp. 50-58.
- W. R. Utz, The Diophantine Equation (x_1 + x_2 + ... + x_n)^2 = x_1^3 + x_2^3 + ... + x_n^3, Fibonacci Quarterly 15:1 (1977), pp. 14, 16. Part 1, part 2.
Programs
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PARI
a(n)=my(v=vector(n, i, 1), N=n^(4/3), m=n); while(v[#v]
Formula
n <= a(n) <= n^(4/3), see A158649.
Comments