A189481 - OEIS

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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

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OFFSET

1,1

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.

FORMULA