A241859 1st Arithmetic derivative of numbers with prime arithmetic derivative (A157037).

5, 7, 13, 31, 19, 41, 31, 61, 59, 71, 43, 71, 101, 61, 101, 73, 113, 103, 151, 131, 103, 109, 191, 131, 167, 211, 151, 151, 139, 241, 167, 191, 151, 227, 271, 199, 191, 181, 311, 269, 193, 167, 433, 199, 211, 269, 311, 293, 281, 229, 191, 263, 401, 241, 251

Offset: 1

Author

Freimut Marschner, Apr 30 2014

Keywords

• nonn

Comments

The arithmetic derivative of numbers with prime arithmetic derivative (A157037) leads to a sequence of a selection of prime numbers. It is possible for several numbers to produce the same primes (see A189441). The next arithmetic derivative is A000012, the simplest sequence of positive numbers: the all 1's sequence, A000012=(A157037)’’.

For the arithmetic derivative of n see A003415. - Wolfdieter Lang, May 10 2014

Examples

			a(10) = (A157037(10))'= (78)' =  (2*3*13)' = 2*3+3*13+2*13 = 71,
a(12) = (A157037(12))'= (105)' = (3*5*7)' = 3*5+5*7+3*7 = 71.
		

Links

• Freimut Marschner, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A157037, A003415, A189441.

Formula

a(n) = (A157037(n))’.

a(n) = A003415(A157037(n)).