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

1,1

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.

Links

Table of n, a(n) for n=1..34.

Example

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.

Sequence in context: A135367 A141493 A103118 * A372697 A372514 A262969

Adjacent sequences: A346137 A346138 A346139 * A346141 A346142 A346143

Keyword

nonn,more

Author

Scott R. Shannon, Jul 05 2021

Status

approved