%I #14 Nov 28 2022 17:22:19

%S 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,

%T 59,61,62,63,67,70,71,73,74,79,83,86,89,97,99,101,103,107,109,113,117,

%U 122,127,131,134,137,139,146,149,151,153,154,157,158,163,167,173,179,181,186,190,191,193,194,195

%N 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.

%C 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.

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F {k | A358235(k) = A038548(k)}.

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

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

%Y Cf. A000040 (subsequence), A003415, A049345, A358235, A358672 (characteristic function), A358674 (complement).

%Y Cf. also A358671.

%K nonn,base

%O 1,2

%A _Antti Karttunen_, Nov 26 2022