A046460 Number of prime factors of concatenation of numbers from 1 up to n, with multiplicity.

0, 3, 2, 2, 3, 8, 2, 5, 4, 3, 6, 6, 3, 3, 3, 4, 5, 6, 6, 10, 8, 6, 4, 6, 5, 9, 8, 7, 4, 7, 3, 6, 6, 2, 8, 9, 4, 4, 6, 9, 5, 7, 4, 7, 10, 7, 5, 8, 6, 10, 3, 9, 8, 14, 5, 5, 6, 4, 4, 8, 3, 8, 5, 10, 6, 8, 3, 10, 7, 6, 6, 7, 3, 9, 6, 6, 5, 6, 6, 10, 6, 7, 6, 7, 6

Offset: 1

Author

Patrick De Geest, Aug 15 1998

Keywords

• nonn
• hard
• base

Links

• Patrick De Geest, Normal Smarandache Concatenated Numbers, Prime factors from 1 up to n
• 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 & Problems Connection.

Crossrefs

Cf. A007908, A046461, A046462, A046463, A046464, A046465, A046466, A046467, A046468, A048288.

Programs

Mathematica

Join[{1},Table[PrimeOmega[FromDigits[Flatten[IntegerDigits[Range[i]]]]],{i,2,35}]] (* Jayanta Basu, Jun 02 2013 *)

PARI

conc(n) = my(s=""); for(k=1, n, s=Str(s, k)); eval(s); \\ A007908
a(n) = bigomega(conc(n)); \\ Michel Marcus, Oct 16 2019

Extensions

Offset 1 and a(1)=0 from Michel Marcus, Oct 16 2019

More terms from Sean A. Irvine, Apr 10 2021