A379397 - OEIS

A379397

Numbers that can be written in exactly two different ways as a sum of at most nine positive third powers.

8, 9, 16, 27, 28, 29, 30, 32, 33, 34, 36, 37, 40, 41, 42, 43, 44, 48, 49, 51, 54, 55, 57, 58, 59, 60, 61, 62, 63, 66, 69, 71, 73, 74, 76, 77, 78, 79, 80, 85, 87, 88, 90, 95, 101, 102, 103, 104, 106, 109, 111, 114, 115, 116, 117, 122, 123, 239

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OFFSET

1,1

COMMENTS

The 'nine' is not arbitrary. Waring stated that every natural number can be expressed as a sum of at most nine cubes (cf. A002804).

LINKS

Table of n, a(n) for n=1..58.

Wikipedia, Waring's Problem

Eric Weisstein's World of Mathematics, Waring's Problem

Index entries for sequences related to sums of cubes

EXAMPLE

29 is in the sequence since 1^3 + 1^3 + 3^3 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 2^3 + 2^3.

123 is in the sequence since 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 4^3.

PROG

(PARI) upto(n) = my(v=vector(n), maxb=sqrtnint(n, 3)); forvec(x=vector(9, i, [0, maxb]), s=sum(i=1, 9, x[i]^3); if(0<s && s<=n, v[s]++); , 1); select(x->x==2, v, 1) \\ David A. Corneth, Dec 23 2024

CROSSREFS

Cf. A002804, A025453, A379396, A379398, A379399, A379400.

Sequence in context: A145820 A385557 A385558 * A227647 A175053 A350075

Adjacent sequences: A379394 A379395 A379396 * A379398 A379399 A379400

KEYWORD

nonn,more

AUTHOR

Patrick De Geest, Dec 22 2024

STATUS

approved