A048288 - OEIS

%I #14 Sep 04 2021 09:57:08

%S 0,2,2,2,3,2,2,4,5,3,2,3,3,4,6,4,7,10,4,5,4,5,4,5,6,9,9,5,7,8,3,6,5,7,

%T 9,8,4,3,6,5,8,6,3,8,7,5,7,7,3,6,3,7,12,14,3,5,4,6,3,3,5,9,6,6,7,7,4,

%U 8,8,4,9,5,7,8,10,3,7,6,4,9,10,1,3,8,3

%N Number of prime factors counted with multiplicity of the reverse concatenation of numbers from 1 to n.

%H Sean A. Irvine, <a href="/A048288/b048288.txt">Table of n, a(n) for n = 1..106</a>

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/revfact.htm">Reversed Smarandache Concatenated Numbers</a>

%H M. Fleuren, <a href="http://www.gallup.unm.edu/~smarandache/michafleuren.htm">Factors and primes of Smarandache sequences</a>.

%H M. Fleuren, <a href="http://www.gallup.unm.edu/~smarandache/micha.txt">Smarandache Factors and Reverse factors</a>

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_008.htm">Puzzle 8. Primes by Listing</a>, The Prime Puzzles and Problems Connection.

%F a(n) = A001222(A000422(n)). - _Michel Marcus_, Jun 14 2021

%e 21 = 3*7 so a(2) = 2; 321 = 3*107 so a(3) = 2; 4321 = 29*149 so a(4) = 2; etc.

%e a(1)=0 since 1 has no prime factors.

%t Join[{0},Table[PrimeOmega[FromDigits[Flatten[IntegerDigits[Range[i,1,-1]]]]],{i,2,36}]] (* _Jayanta Basu_, May 30 2013 *)

%Y Cf. A000422, A001222, A046460, A046461, A046468, A050679, A050680, A050681, A050682.

%K nonn,base

%O 1,2

%A Paul Jasper (jasperpaul(AT)hotmail.com)

%E Offset and a(19) corrected and more terms from _Sean A. Irvine_, Jun 13 2021

%E Edited by _N. J. A. Sloane_, Sep 04 2021