A346140 Numbers m such that there exist positive integers i <= m and j >= m such that m = Sum_{k=i..j} A001065(k), where A001065(k) = sum of the proper divisors of k, and i and j do not both equal m.

2, 4, 5, 7, 8, 16, 29, 32, 39, 121, 128, 256, 279, 469, 1299, 3477, 7299, 7525, 8192, 13969, 19262, 19909, 26739, 31493, 54722, 65536, 99381, 131072, 357699, 524288, 13204262, 20742483, 33550337, 72873362

Offset: 1

Author

Scott R. Shannon, Jul 05 2021

Keywords

• nonn
• more

Comments

No perfect numbers are included as it is required i and j cannot both equal m. Any prime number that is one more than a perfect number will appear in the sequence.

Examples

			2 is a term as A001065(2) = 1, A001065(3) = 1, and 1 + 1 = 2.
5 is a term as A001065(3) = 1, A001065(4) = 3, A001065(5) = 1, and 1 + 3 + 1 = 5.
29 is a term as A001065(28) = 28, A001065(29) = 1, and 28 + 1 = 29. This is an example of a prime number one more than a perfect number, thus it will appear in the sequence.
121 is a term as A001065(121) = 12, A001065(122) = 64, A001065(123) = 45, and 12 + 64 + 45 = 121.
19262 is a term as A001065(19261) = 3203, A001065(19262) = 9634, A001065(19263) = 6425, and 3203 + 9634 + 6425 = 19262. This is the first term that requires i < m and j > m.
		

Crossrefs

Cf. A001065, A000396, A072188.