A378271 Number of partitions of 1 into {1/1^3, 1/2^3, 1/3^3, ..., 1/n^3}.

1, 2, 3, 11, 12, 435, 436, 6748, 42360, 1252676, 1252677, 302302546, 302302547

Offset

1,2

Links

Table of n, a(n) for n=1..13.

Index entries for sequences related to Egyptian fractions

Formula

a(p) = a(p-1) + 1 for prime p. - Jinyuan Wang, Dec 11 2024

Example

a(4) = 11 because we have 64 * (1/64) = 56 * (1/64) + 1/8 = 48 * (1/64) + 2 * (1/8) = 40 * (1/64) + 3 * (1/8) = 32 * (1/64) + 4 * (1/8) = 24 * (1/64) + 5 * (1/8) = 16 * (1/64) + 6 * (1/8) = 8 * (1/64) + 7 * (1/8) = 27 * (1/27) = 8 * (1/8) = 1.

Crossrefs

Cf. A000578, A020473, A038034, A378270.

Sequence in context: A227764 A135115 A107402 * A082618 A382862 A020610

Adjacent sequences: A378268 A378269 A378270 * A378272 A378273 A378274

Keyword

nonn,more

Author

Ilya Gutkovskiy, Nov 21 2024

Extensions

a(9)-a(13) from Jinyuan Wang, Dec 11 2024

Status

approved