A358673 Numbers k such that for all factorizations of k as x*y, the sum (x * y') + (x' * y) is carryfree when the addition is done in the primorial base, A049345. Here n' stands for A003415(n), the arithmetic derivative of n.

1, 2, 3, 4, 5, 6, 7, 11, 12, 13, 14, 17, 18, 19, 23, 26, 27, 29, 31, 37, 38, 41, 43, 47, 53, 59, 61, 62, 63, 67, 70, 71, 73, 74, 79, 83, 86, 89, 97, 99, 101, 103, 107, 109, 113, 117, 122, 127, 131, 134, 137, 139, 146, 149, 151, 153, 154, 157, 158, 163, 167, 173, 179, 181, 186, 190, 191, 193, 194, 195

Offset: 1

Author

Antti Karttunen, Nov 26 2022

Keywords

• nonn
• base

Comments

Numbers k such that there are no factorization of k into such a pair of natural numbers x and y, that the sum (x * A003415(y)) + (A003415(x) * y) would generate any carries when the addition is done in the primorial base.

Examples

			Refer to the examples in A358235 to see why 6 and 63 are terms of this sequence, while 24 is not.
See also examples in A380525.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A003415, A049345, A358235, A358672 (characteristic function), A358674 (complement).

Subsequences: A000040, A380525 (squarefree terms), A380468.

Cf. also A358671.

Programs

PARI

isA358673(n) = A358672(n);

Formula

{k such that A358235(k) = A038548(k)}.