A373687 a(n) is the number of ways n can be written as a sum of a practical number and two pentagonal numbers.

1, 2, 2, 2, 1, 3, 3, 3, 2, 2, 2, 3, 3, 5, 1, 3, 3, 6, 3, 3, 4, 3, 3, 5, 6, 5, 1, 6, 6, 7, 4, 4, 5, 4, 5, 6, 6, 6, 3, 7, 7, 10, 5, 5, 5, 6, 5, 8, 4, 5, 4, 9, 8, 8, 7, 7, 5, 8, 8, 9, 4, 6, 6, 11, 8, 8, 7, 7, 6, 6, 9, 12, 5, 8, 8, 12, 10, 8, 9, 7

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. A000326, A005153.

Sequence in context: A359930 A269400 A130267 * A060610 A352671 A351581

Adjacent sequences: A373684 A373685 A373686 * A373688 A373689 A373690

Keyword

nonn

Author

Duc Van Khanh Tran, Jun 13 2024

Status

approved