A373686 a(n) is the number of ways n can be written as a sum of a practical number and two squares.

1, 2, 2, 2, 2, 4, 2, 3, 3, 4, 3, 4, 3, 4, 2, 4, 5, 5, 4, 6, 6, 6, 2, 6, 5, 7, 4, 7, 7, 6, 5, 7, 9, 7, 4, 8, 9, 10, 2, 9, 10, 9, 6, 9, 9, 8, 5, 8, 10, 9, 5, 10, 11, 9, 7, 12, 11, 11, 6, 9, 11, 10, 3, 11, 14, 13, 9, 12, 13, 11, 7, 10, 15, 14, 4, 13, 13, 8, 8, 15

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. A000290, A005153.

Sequence in context: A046927 A366563 A351411 * A084718 A154851 A281854

Adjacent sequences: A373683 A373684 A373685 * A373687 A373688 A373689

Keyword

nonn

Author

Duc Van Khanh Tran, Jun 13 2024

Status

approved