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A003330
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Numbers that are the sum of 7 positive cubes.
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38
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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a(n) = n + 208 for all n > 2200. - M. F. Hasler, Aug 23 2020
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EXAMPLE
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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)
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)
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PROG
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(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
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CROSSREFS
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Other sequences of numbers that are the sum of x nonzero y-th powers:
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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More terms from Arlin Anderson (starship1(AT)gmail.com)
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STATUS
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approved
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