A048288 Number of prime factors counted with multiplicity of the reverse concatenation of numbers from 1 to n.

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

Offset: 1

Author

Paul Jasper (jasperpaul(AT)hotmail.com)

Keywords

• nonn
• base

Examples

			21 = 3*7 so a(2) = 2; 321 = 3*107 so a(3) = 2; 4321 = 29*149 so a(4) = 2; etc.
a(1)=0 since 1 has no prime factors.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..106
• Patrick De Geest, Reversed Smarandache Concatenated Numbers
• M. Fleuren, Factors and primes of Smarandache sequences.
• M. Fleuren, Smarandache Factors and Reverse factors
• Carlos Rivera, Puzzle 8. Primes by Listing, The Prime Puzzles and Problems Connection.

Crossrefs

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

Programs

Mathematica

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

Formula

a(n) = A001222(A000422(n)). - Michel Marcus, Jun 14 2021

Extensions

Offset and a(19) corrected and more terms from Sean A. Irvine, Jun 13 2021

Edited by N. J. A. Sloane, Sep 04 2021