A370513 Complement of A323599.

2, 5, 29, 39, 53, 59, 73, 95, 119, 123, 125, 129, 137, 145, 147, 149, 157, 159, 163, 173, 179, 191, 199, 207, 209, 213, 219, 221, 235, 251, 257, 263, 265, 269, 271, 279, 291, 293, 299, 303, 305, 325, 327, 329, 343, 345, 347, 359, 365, 367, 369, 375, 385, 395, 397

Offset: 1

Author

Torlach Rush, Feb 20 2024

Keywords

• nonn

Comments

Terms of this sequence are not solutions of Sum_{d|k} A069359(d), k >= 1.

Proof that 2 is not a solution of Sum_{d|k} A069359(d), k >= 1: (Start)

If 2 is a solution then the only summands of the above are either (0,2) or (0,1,1).

(0,2) cannot be the only summands. If 2 is a summand then it is also a divisor of a(n) and A069359(2) = 1. If 2 is a summand then so must 1 be a summand.

(0,1,1) cannot be the only summands. There must exist an additional summand A069359(p_1*p_2) where p_1 and p_2 (primes) contribute to each 1 in (0,1,1).

(End)

To prove that 5 is not a solution of Sum_{d|k} A069359(d), k >= 1 we need to show that each of the following summands cannot exist: (0,5), (0,1,4), (0,1,2,2), (0,1,1,3), (0,1,1,1,2). (0,1,1,1,1,1). Following from the above proof this is elementary.

Examples

			2 is a term because it is not a solution of Sum_{d|k} A069359(d), k >= 1. See proof in Comments.
		

Crossrefs

Cf. A069359, A323599.