A370125 Numbers k such that the least prime dividing the arithmetic derivative of k is equal to the least prime not dividing k.

1, 6, 9, 14, 15, 21, 25, 26, 33, 35, 38, 39, 49, 50, 51, 55, 57, 62, 65, 69, 74, 77, 81, 85, 86, 87, 91, 93, 95, 110, 111, 115, 119, 121, 122, 123, 129, 133, 134, 135, 141, 143, 145, 146, 155, 158, 159, 161, 169, 170, 177, 183, 185, 187, 189, 194, 201, 203, 205, 206, 209, 213, 215, 217, 218, 219, 221, 225, 230, 235

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Example

The initial term 1 is included because A003415(1) = 0, every prime divides zero, including the smallest of primes, which is 2, and 2 is also the least prime that does not divide 1.
6 = 2*3 is included because the smallest prime that does not divide it is 5, and 5 is also the smallest prime dividing 6' = 5.
14 = 2*7 is included because the smallest prime dividing 14' = 2+7 = 9 is 3, which is also the smallest prime not dividing 14.

Prog

(PARI) \\ See A370124.

Crossrefs

Cf. A003415, A020639, A053669, A276086, A370124 (characteristic function).

Cf. A016754 (subsequence).

Sequence in context: A155705 A267369 A177891 * A367947 A228804 A315975

Adjacent sequences: A370122 A370123 A370124 * A370126 A370127 A370128

Keyword

nonn

Author

Antti Karttunen, Feb 21 2024

Status

approved