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