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A373687
a(n) is the number of ways n can be written as a sum of a practical number and two pentagonal numbers.
1
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
Sai Teja Somu and Duc Van Khanh Tran, On sums of practical numbers and polygonal numbers, Journal of Integer Sequences, 27(5), 2024.
CROSSREFS
Sequence in context: A359930 A269400 A130267 * A060610 A352671 A351581
KEYWORD
nonn
AUTHOR
Duc Van Khanh Tran, Jun 13 2024
STATUS
approved