A189481 Numbers n such that x' = n has a unique solution, where x' denotes the arithmetic derivative (A003415).

4, 5, 6, 7, 8, 9, 13, 15, 19, 25, 27, 33, 41, 43, 49, 51, 59, 63, 69, 73, 77, 85, 95, 99, 105, 109, 113, 115, 121, 133, 135, 139, 141, 143, 153, 155, 159, 161, 169, 171, 175, 181, 187, 193, 201, 203, 225, 227, 229, 235, 239, 249, 251, 253, 259, 265, 267, 273

Offset: 1

Author

T. D. Noe, Apr 22 2011

Keywords

• nonn

Comments

The unique solutions are in A189482. Ufnarovski and Ahlander list these numbers on page 7 of their paper.

Interestingly, for about half the numbers n in this sequence, the unique solution is x = 2(n-2) because n-2 is prime.

References

• See A003415.

Links

• T. D. Noe, Table of n, a(n) for n = 1..5000
• Victor Ufnarovski and Bo Ahlander, How to Differentiate a Number, J. Integer Seqs., Vol. 6, 2003.

Crossrefs

Cf. A003415, A099302, A189482.

Formula

n such that A099302(n) = 1.