cp's OEIS Frontend

A050252 Number of digits in the prime factorization of n (counting terms of the form p^1 as p).

%I A050252 #34 Feb 18 2025 18:56:44
%S A050252 1,1,1,2,1,2,1,2,2,2,2,3,2,2,2,2,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,2,3,3,
%T A050252 2,4,2,3,3,3,2,3,2,4,3,3,2,3,2,3,3,4,2,3,3,3,3,3,2,4,2,3,3,2,3,4,2,4,
%U A050252 3,3,2,4,2,3,3,4,3,4,2,3,2,3,2,4,3,3,3,4,2,4,3,4,3,3,3,3,2,3,4,4,3,4
%N A050252 Number of digits in the prime factorization of n (counting terms of the form p^1 as p).
%H A050252 Reinhard Zumkeller, <a href="/A050252/b050252.txt">Table of n, a(n) for n = 1..10000</a>
%H A050252 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeFactorization.html">Prime Factorization</a>.
%F A050252 a(A192010(n)) = n and a(m) != n for m < A192010(n);
%F A050252 a(A046759(n)) < A055642(A046759(n)); a(A046758(n)) = A055642(A046758(n)); a(A046760(n)) > A055642(A046760(n)). [_Reinhard Zumkeller_, Jun 21 2011]
%t A050252 nd[n_]:=Total@IntegerLength@Select[Flatten@FactorInteger[n],#>1&];Table[If[n==1,1,nd[n]],{n,102}] (* _Vladimir Joseph Stephan Orlovsky_, Jan 30 2012 *)
%o A050252 (Haskell)
%o A050252 a050252 1 = 1
%o A050252 a050252 n = sum $ map a055642 $
%o A050252             (a027748_row n) ++ (filter (> 1) $ a124010_row n)
%o A050252 -- _Reinhard Zumkeller_, Aug 03 2013, Jun 21 2011
%o A050252 (Python)
%o A050252 from sympy import factorint
%o A050252 def a(n): return 1 if n == 1 else sum(len(str(p))+(len(str(e)) if e>1 else 0) for p, e in factorint(n).items())
%o A050252 print([a(n) for n in range(1, 103)]) # _Michael S. Branicky_, Dec 27 2024
%Y A050252 Cf. A046758, A073048, A055642, A020639, A027748, A124010, A110475.
%Y A050252 Cf. also A377369 (analog for base 2).
%K A050252 nonn,base
%O A050252 1,4
%A A050252 _Eric W. Weisstein_