b = {}; a = {}; Do[w = RealDigits[n]; w = First[w]; Do[AppendTo[a, w[[k]]], {k, 1, Length[w]}]; p = FromDigits[a]; m = FactorInteger[p]; AppendTo[b, Length[m]], {n, 1, 20}]; b - _(* _Artur Jasinski_, Mar 30 2008 *)
Table[PrimeNu[FromDigits[Flatten[IntegerDigits[Range[n]]]]], {n, 30}] (* Jan Mangaldan, Jul 07 2020 *)
approved
editing
b = {}; a = {}; Do[w = RealDigits[n]; w = First[w]; Do[AppendTo[a, w[[k]]], {k, 1, Length[w]}]; p = FromDigits[a]; m = FactorInteger[p]; AppendTo[b, Length[m]], {n, 1, 20}]; b - _Artur Jasinski (grafix(AT)csl.pl), _, Mar 30 2008
Terms 59-100 from _Sean A. Irvine (sairvin(AT)xtra.co.nz), _, Nov 04 2009
Edited and extended by _Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), _, Mar 29 2006
_Parthasarathy Nambi (PachaNambi(AT)yahoo.com), _, Mar 20 2006
0, 2, 2, 2, 3, 3, 2, 4, 3, 3, 6, 4, 3, 3, 3, 3, 4, 5, 6, 6, 8, 6, 4, 5, 4, 6, 5, 5, 4, 7, 3, 5, 6, 2, 7, 5, 4, 4, 6, 8, 5, 7, 4, 4, 9, 7, 5, 7, 6, 9, 3, 3, 4, 9, 5, 4, 6, 4, 4, 6, 3, 7, 4, 9, 6, 8, 3, 7, 7, 6, 5, 5, 3, 9, 5, 4, 5, 6, 6, 7, 4, 7, 6, 3, 5, 7, 6, 5, 9, 8, 6, 6, 7, 5, 6, 5, 2, 9, 5, 9
nonn,base,more,new
Terms 59-100 from Sean A. Irvine (sairvin(AT)xtra.co.nz), Nov 04 2009
b = {}; a = {}; Do[w = RealDigits[n]; w = First[w]; Do[AppendTo[a, w[[k]]], {k, 1, Length[w]}]; p = FromDigits[a]; m = FactorInteger[p]; AppendTo[b, Length[m]], {n, 1, 20}]; b (*Artur Jasinski*) - Artur Jasinski (grafix(AT)csl.pl), Mar 30 2008
nonn,base,more,new
b = {}; a = {}; Do[w = RealDigits[n]; w = First[w]; Do[AppendTo[a, w[[k]]], {k, 1, Length[w]}]; p = FromDigits[a]; m = FactorInteger[p]; AppendTo[b, Length[m]], {n, 1, 20}]; b (*Artur Jasinski*) - Artur Jasinski (grafix(AT)csl.pl), Mar 30 2008
nonn,base,more,new
Number of distinct prime divisors of the concatenation of 1,...,n.
0, 2, 2, 2, 3, 3, 2, 4, 3, 3, 6, 4, 3, 3, 3, 3, 4, 5, 6, 6, 8, 6, 4, 5, 4, 6, 5, 5, 4, 7, 3, 5, 6, 2, 7, 5, 4, 4, 6, 8, 5, 7, 4, 4, 9, 7, 5, 7, 6, 9, 3, 3, 4, 9, 5, 4, 6, 4
1,2
Dario Alpern's factorization program was used for n > 43.
D. Alpern, <a href="http://www.alpertron.com.ar/ecm.htm">Factorization using the Elliptic Curve Method</a>
123456 = 2*2*2*2*2*2*3*643, distinct prime divisors are 2, 3 and 643, hence a(6) = 3.
(PARI) {a=""; for(n=1, 43, a=concat(a, n); print1(omega(eval(a)), ", "))}
nonn,base,more
Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Mar 20 2006
Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 29 2006
approved