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A359829
Primitive elements of A235992: numbers k with an even arithmetic derivative that cannot be represented as a product of two smaller such numbers.
4
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 17 2023
STATUS
approved