cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A335018 Number of triples (d1,d2,d3) where each element is a divisor of m and d1 + d2 + d3 <= m where m is least odd integer of each prime signature.

Original entry on oeis.org

0, 1, 8, 27, 27, 125, 64, 343, 343, 512, 125, 1331, 729, 1331, 216, 3375, 3375, 1331, 4913, 2744, 343, 6859, 3375, 12167, 2197, 12167, 4913, 512, 12167, 6859, 29791, 3375, 17576, 24389, 29791, 42875, 8000, 729, 29791, 19683, 12167, 59319, 4913, 42875, 42875, 103823, 13824
Offset: 1

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Author

David A. Corneth, May 19 2020

Keywords

Comments

All terms are cubes. Proof: Let d_k be the k-th divisor of some odd m > 1 and t be the number of divisors of m. Then d_(t-1) is <= n/3 and so any sum of 3 divisors of at most d_(t-1) is at most n and so that sum is counted per A093035. A sum of 3 divisors of m where one of the divisors is d_t = m as more than m so not counted. This gives (t-1)^3 possible triples hence all terms are cubes.

Examples

			A147516(6) = 45 so a(6) = A093035(45) = (tau(45) - 1)^3.

Crossrefs

Cf. A000005, A093035, A147516.

Formula

a(n) = A093035(A147516(n)).
a(n) = A000005(A147516(n) - 1)^3.
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