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

1,2

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.

Formula

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A284565 A227911 A325783 * A050677 A058013 A223934

Adjacent sequences: A048285 A048286 A048287 * A048289 A048290 A048291

Keyword

nonn,base

Author

Paul Jasper (jasperpaul(AT)hotmail.com)

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

Status

approved