login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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.
4

%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