

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.


0



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
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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 * A262969 A158029 A217378
Adjacent sequences: A346137 A346138 A346139 * A346141 A346142 A346143


KEYWORD

nonn,more


AUTHOR

Scott R. Shannon, Jul 05 2021


STATUS

approved



