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

1,1

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.

Links

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

Example

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

Prog

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

Crossrefs

Cf. A003415, A157037.

Sequence in context: A036798 A119434 A091495 * A308779 A046405 A128278

Adjacent sequences: A256670 A256671 A256672 * A256674 A256675 A256676

Keyword

nonn

Author

M. F. Hasler, Apr 07 2015

Status

approved