A256673 - OEIS

%I #11 Apr 08 2015 11:22:16

%S 105,165,231,255,273,285,345,357,385,399,455,465,483,555,561,595,609,

%T 645,651,663,665,715,795,805,861,885,915,957,969,987,1001,1015,1023,

%U 1045,1095,1131,1185,1281,1295,1309,1311,1335,1353,1407,1443,1463,1479,1495,1515,1533,1545,1547,1551,1615,1635,1645

%N Odd numbers with prime arithmetic derivative A003415.

%C The subsequence of odd numbers in A157037.

%C 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.

%H Reinhard Zumkeller, <a href="/A256673/b256673.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (Haskell)

%o a256673 n = a256673_list !! (n-1)

%o a256673_list = filter odd a157037_list

%o -- _Reinhard Zumkeller_, Apr 08 2015

%Y Cf. A003415, A157037.

%K nonn

%O 1,1

%A _M. F. Hasler_, Apr 07 2015