cp's OEIS Frontend

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.

%I A358673 #22 Feb 09 2025 18:10:03
%S A358673 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 A358673 59,61,62,63,67,70,71,73,74,79,83,86,89,97,99,101,103,107,109,113,117,
%U A358673 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 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.
%C A358673 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 A358673 Antti Karttunen, <a href="/A358673/b358673.txt">Table of n, a(n) for n = 1..20000</a>
%H A358673 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%F A358673 {k such that A358235(k) = A038548(k)}.
%e A358673 Refer to the examples in A358235 to see why 6 and 63 are terms of this sequence, while 24 is not.
%e A358673 See also examples in A380525.
%o A358673 (PARI) isA358673(n) = A358672(n);
%Y A358673 Cf. A003415,  A049345, A358235, A358672 (characteristic function), A358674 (complement).
%Y A358673 Subsequences: A000040, A380525 (squarefree terms), A380468.
%Y A358673 Cf. also A358671.
%K A358673 nonn,base
%O A358673 1,2
%A A358673 _Antti Karttunen_, Nov 26 2022