A189555 Numbers n such that x' = n has two solutions, where x' is the arithmetic derivative (A003415) of x.

10, 12, 14, 18, 20, 21, 28, 31, 38, 39, 45, 55, 61, 71, 81, 87, 101, 103, 111, 119, 123, 129, 131, 147, 183, 185, 199, 211, 213, 215, 241, 243, 255, 269, 291, 297, 299, 327, 339, 343, 351, 355, 359, 361, 363, 381, 395, 399, 401, 411, 421, 433, 439, 471, 493

Offset: 1

Author

T. D. Noe, Apr 24 2011

Keywords

• nonn

Comments

Ufnarovski and Ahlander conjecture that this sequence, and any such sequence that has numbers n such that x' = n has k solutions, is infinite. See A098700 and A189481 for the k=0 and 1 cases. It appears that the only even terms here are 10, 12, 14, 18, 20, 28, and 38. The prime terms are in A189556.

References

• See A003415.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Victor Ufnarovski and Bo Ahlander, How to Differentiate a Number, J. Integer Seqs., Vol. 6, 2003.

Crossrefs

Cf. A003415, A098700 (no solution), A099302, A189481 (1 solution).

Formula

n such that A099302(n) = 2.