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

1,2

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to primorial base.

Formula

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

Example

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.

Prog

(PARI) isA358673(n) = A358672(n);

Crossrefs

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

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

Cf. also A358671.

Sequence in context: A275910 A032971 A099466 * A032976 A174219 A115037

Adjacent sequences: A358670 A358671 A358672 * A358674 A358675 A358676

Keyword

nonn,base

Author

Antti Karttunen, Nov 26 2022

Status

approved