1,2

Number of factorial divisors of n. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Oct 19 2002

The sequence may be constructed as follows. Step 1: start with 1, concatenate and add+1 to last term gives: 1,2. Step 2: 2 is the last term so concatenate twice those terms and add +1 to last term gives: 1,2,1,2,1,3 we get 6 terms. Step 3: 3 is the last term, concatenate 3 times those 6 terms and add +1 to last term gives: 1,2,1,2,1,3,1,2,1,2,1,3,1,2,1,2,1,3,1,2,1,2,1,4, iterates. At k-th step we obtain (k+1)! terms.- Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 11 2003

Comment from Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 17 2007: "Another way to construct the sequence : start from an infinite series of 1's:

"1,1,1,1,1,1,1,1,1,1,1,1,... replace every 2 ones by a 2 giving:

"1,2,1,2,1,2,1,2,1,2,1,2,... replace every 3 twos by a 3 giving:

"1,2,1,2,1,3,1,2,1,2,1,3,... replace every 4 threes by a 4 etc."

Joerg Arndt, Fxtbook

Claude Lenormand, Comments on this sequence

J. Sandor, On Additive Analogues of Certain Arithmetic Smarandache Functions.

G.f.: Sum_{k>0} x^(k!)/(1-x^(k!)). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Dec 13 2002

a(12) = 3 because 3! is highest factorial to divide 12.

Cf. A055874, A055926, A055770, A073575.

Adjacent sequences: A055878 A055879 A055880 this_sequence A055882 A055883 A055884

Sequence in context: A048220 A078380 A062356 this_sequence A055874 A066451 A091090

easy,nonn

Leroy Quet (qq-quet(AT)mindspring.com) and Labos E. (labos(AT)ana.sote.hu), Jul 16 2000