A256673 Odd numbers with prime arithmetic derivative A003415.

105, 165, 231, 255, 273, 285, 345, 357, 385, 399, 455, 465, 483, 555, 561, 595, 609, 645, 651, 663, 665, 715, 795, 805, 861, 885, 915, 957, 969, 987, 1001, 1015, 1023, 1045, 1095, 1131, 1185, 1281, 1295, 1309, 1311, 1335, 1353, 1407, 1443, 1463, 1479, 1495, 1515, 1533, 1545, 1547, 1551, 1615, 1635, 1645

Offset: 1

Author

M. F. Hasler, Apr 07 2015

Keywords

• nonn

Comments

The subsequence of odd numbers in A157037.

In order to have a prime arithmetic derivative (satisfying (mn)' = m'n + m n', p' = 1 for primes), an odd number must have at least 3 distinct prime factors.

Examples

			a(1)=105 is the smallest odd number with prime arithmetic derivative A003415(3*5*7) = 5*7 + 3*7 + 3*5 = 71.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003415, A157037.

Programs

Haskell

a256673 n = a256673_list !! (n-1)
a256673_list = filter odd a157037_list
-- Reinhard Zumkeller, Apr 08 2015