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A003330
Numbers that are the sum of 7 positive cubes.
38
7, 14, 21, 28, 33, 35, 40, 42, 47, 49, 54, 56, 59, 61, 66, 68, 70, 73, 75, 77, 80, 84, 85, 87, 91, 92, 94, 96, 98, 99, 103, 105, 106, 110, 111, 112, 113, 117, 118, 122, 124, 125, 129, 131, 132, 133, 136, 137, 138, 140, 143, 144, 145, 147, 148, 150, 151, 152, 154
OFFSET
1,1
COMMENTS
As the order of addition doesn't matter we can assume terms are in increasing order. - David A. Corneth, Aug 01 2020
2408 is the largest among only 208 positive integers not in this sequence: cf. formula. - M. F. Hasler, Aug 23 2020
FORMULA
a(n) = n + 208 for all n > 2200. - M. F. Hasler, Aug 23 2020
EXAMPLE
From M. F. Hasler, Aug 23 2020: (Start)
The first few terms are multiples of 7 because of the coincidence that 2^3 - 1^3 = 7, equal to the number of cubes we consider here:
7 = 1^3 * 7 is the smallest sum of seven positive cubes.
14 = 1^3 * 6 + 2^3 = 6 + 8 is the next larger sum of seven positive cubes.
21 = 1^3 * 5 + 2^3 * 2 = 5 + 16 is the next larger sum of seven positive cubes.
28 = 1^3 * 4 + 2^3 * 3 = 4 + 24 is the next larger sum of seven positive cubes.
There are three more terms of this form, but the next larger sum of seven positive cubes is a(5) = 3^3 + 6 * 1^3 = 33. (End)
From David A. Corneth, Aug 01 2020: (Start)
2070 is in the sequence as 2070 = 4^3 + 4^3 + 4^3 + 5^3 + 8^3 + 8^3 + 9^3.
2383 is in the sequence as 2383 = 3^3 + 5^3 + 5^3 + 6^3 + 6^3 + 7^3 + 11^3.
3592 is in the sequence as 3592 = 4^3 + 5^3 + 6^3 + 9^3 + 9^3 + 9^3 + 10^3. (End)
PROG
(PARI) (A003330_upto(N, k=7, m=3)=[i|i<-[1..#N=sum(n=1, sqrtnint(N, m), 'x^n^m, O('x^N))^k], polcoef(N, i)])(160) \\ M. F. Hasler, Aug 02 2020
CROSSREFS
Other sequences of numbers that are the sum of x nonzero y-th powers:
A000404 (x=2, y=2), A000408 (3, 2), A000414 (4, 2), A047700 (5, 2),
A003325 (2, 3), A003072 (3, 3), A003327 .. A003335 (4 .. 12, 3),
A003336 .. A003346 (2 .. 12, 4), A003347 .. A003357 (2 .. 12, 5),
A003358 .. A003368 (2 .. 12, 6), A003369 .. A003379 (2 .. 12, 7),
A003380 .. A003390 (2 .. 12, 8), A003391 .. A004801 (2 .. 12, 9),
A004802 .. A004812 (2 .. 12, 10), A004813 .. A004823 (2 .. 12, 11).
Sequence in context: A276613 A004939 A115417 * A345773 A037985 A044847
KEYWORD
nonn,easy
EXTENSIONS
More terms from Arlin Anderson (starship1(AT)gmail.com)
STATUS
approved