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

Author

Antti Karttunen, Feb 21 2024

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Cf. A016754 (subsequence).

Programs

PARI

\\ See A370124.