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A373688

a(n) is the number of ways n can be written as a sum of a practical number and two hexagonal numbers.

1, 2, 2, 2, 1, 2, 2, 4, 2, 2, 1, 2, 3, 3, 1, 3, 3, 5, 3, 4, 2, 4, 3, 4, 3, 2, 3, 3, 3, 6, 5, 6, 4, 5, 4, 7, 4, 4, 3, 5, 3, 6, 3, 5, 4, 6, 6, 7, 6, 4, 4, 6, 4, 6, 5, 4, 7, 7, 3, 6, 7, 7, 6, 7, 3, 8, 5, 7, 6, 7, 6, 8, 6, 7, 7, 8, 4, 8, 7, 6

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OFFSET

1,2

COMMENTS

Somu and Tran (2024) proved that a(n) > 0 for sufficiently large n and conjectured that a(n) > 0 for all n > 0. The conjecture was checked up to 10^8.

LINKS

Duc Van Khanh Tran, Table of n, a(n) for n = 1..10000

Sai Teja Somu and Duc Van Khanh Tran, On sums of practical numbers and polygonal numbers, Journal of Integer Sequences, 27(5), 2024.

CROSSREFS

Cf. A000384, A005153.

Sequence in context: A366136 A366693 A147680 * A192895 A210685 A264051

Adjacent sequences: A373685 A373686 A373687 * A373689 A373690 A373691

KEYWORD

nonn

AUTHOR

Duc Van Khanh Tran, Jun 13 2024

STATUS

approved

URL: https://oeis.org/A373688

⇱ A373688 - OEIS