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

1,2

Links

Table of n, a(n) for n=1..85.

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A059942 A032450 A376274 * A327661 A117643 A141862

Adjacent sequences: A046457 A046458 A046459 * A046461 A046462 A046463

Keyword

nonn,hard,base

Author

Patrick De Geest, Aug 15 1998

Extensions

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

More terms from Sean A. Irvine, Apr 10 2021

Status

approved