A358673 - OEIS

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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

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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

Table of n, a(n) for n=1..70.

Index entries for sequences related to primorial base

FORMULA

{k | 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.

PROG

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

CROSSREFS

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

Cf. also A358671.