A319801 Odd numbers without middle divisors.

3, 5, 7, 11, 13, 17, 19, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47, 51, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 75, 79, 83, 85, 87, 89, 93, 95, 97, 101, 103, 105, 107, 109, 111, 113, 115, 119, 123, 125, 127, 129, 131, 133, 137, 139, 141, 145, 147, 149, 151, 155, 157, 159, 161, 163, 167, 171, 173, 175, 177

Offset: 1

Author

Omar E. Pol, Sep 28 2018

Keywords

• nonn

Comments

Odd numbers k such that the symmetric representation of sigma(k) has an even number of parts.

All odd primes (A065091) are in the sequence.

For the definition of middle divisors, see A067742.

For more information about the symmetric representation of sigma(k) see A237593.

Examples

			21 is in the sequence because it's an odd number and the symmetric representation of sigma(21) = 32 has an even number of parts (more exactly four parts), as shown below:
.     _ _ _ _ _ _ _ _ _ _ _ 11
.    |_ _ _ _ _ _ _ _ _ _ _|
.                          |
.                          |
.                          |_ _ _ 5
.                          |_ _  |_
.                              |_ _|_
.                                  | |_ 5
.                                  |_  |
.                                    | |
.                                    |_|_ _ _ _ 11
.                                            | |
.                                            | |
.                                            | |
.                                            | |
.                                            | |
.                                            | |
.                                            | |
.                                            | |
.                                            | |
.                                            | |
.                                            |_|
.
		

Crossrefs

Intersection of A005408 and A071561.

Cf. A000203, A065091, A067742, A071090, A071562, A236104, A237270, A237271, A237593, A239931, A239933, A240542, A245092, A280919, A281007, A296508, A299761, A299777, A303297, A319529, A319796, A319802.