A359829 Primitive elements of A235992: numbers k with an even arithmetic derivative that cannot be represented as a product of two smaller such numbers.

1, 4, 8, 9, 12, 15, 20, 21, 24, 25, 28, 33, 35, 39, 40, 44, 49, 51, 52, 55, 56, 57, 65, 68, 69, 76, 77, 85, 87, 88, 91, 92, 93, 95, 104, 111, 115, 116, 119, 121, 123, 124, 129, 133, 136, 141, 143, 145, 148, 152, 155, 159, 161, 164, 169, 172, 177, 183, 184, 185, 187, 188, 201, 203, 205, 209, 212, 213

Offset

1,2

Links

Table of n, a(n) for n=1..68.

Formula

{k | A358680(k)=1 and 0=Sum_{d|k, 1<d<k} A358680(d)*A358680(k/d)}.

Example

For 12, A003415(12) = 12' = 16, an even number, but on the other hand, for its factors 2 and 6, neither has even derivative as 2' = 1, 6' = 5, while for its factors 3 and 4 only the other factor has even derivative, as 3' = 1, 4' = 4, so 12 has no nontrivial pair of factors such that both of them would have even arithmetic derivative, and therefore 12 is included in this sequence.

Prog

(PARI) isA359829(n) = A359828(n);

Crossrefs

Setwise difference A235992 \ A359831.

Cf. A003415, A358680, A359828 (characteristic function).

Cf. A046315 (subsequence).

Sequence in context: A235992 A362006 A359783 * A221865 A004753 A144794

Adjacent sequences: A359826 A359827 A359828 * A359830 A359831 A359832

Keyword

nonn

Author

Antti Karttunen, Jan 17 2023

Status

approved