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A076558 a(n) = r * min(e_1, ..., e_r), where n = p_1^e_1 . .... p_r^e_r is the canonical prime factorization of n, a(1) = 0.

%I A076558 #26 Sep 09 2024 09:34:49
%S A076558 0,1,1,2,1,2,1,3,2,2,1,2,1,2,2,4,1,2,1,2,2,2,1,2,2,2,3,2,1,3,1,5,2,2,
%T A076558 2,4,1,2,2,2,1,3,1,2,2,2,1,2,2,2,2,2,1,2,2,2,2,2,1,3,1,2,2,6,2,3,1,2,
%U A076558 2,3,1,4,1,2,2,2,2,3,1,2,4,2,1,3,2,2,2,2,1,3,2,2,2,2,2,2,1,2,2,4
%N A076558 a(n) = r * min(e_1, ..., e_r), where n = p_1^e_1 . .... p_r^e_r is the canonical prime factorization of n, a(1) = 0.
%C A076558 Omega(n) >= a(n) for n >= 1, where Omega(n) = the number of prime factors of n, counting multiplicity.
%C A076558 Positions of records are A000079. - _David A. Corneth_, May 05 2020
%H A076558 Antti Karttunen, <a href="/A076558/b076558.txt">Table of n, a(n) for n = 1..10000</a>
%H A076558 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_201.htm">Puzzle #201 The Arithmetic Function A(n)</a>, The Prime Puzzles and Problems Connection.
%H A076558 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A076558 a(n) = A001221(n) * A051904(n). - _Antti Karttunen_, Jul 12 2017
%t A076558 a[n_] := Module[{pf}, pf = Transpose[FactorInteger[n]]; Length[pf[[1]]]*Min[pf[[2]]]]; Table[a[i] - Boole[i == 1], {i, 100}]
%t A076558 (* Second program: *)
%t A076558 Table[Length[#] Min[#] - Boole[n == 1] &@ FactorInteger[n][[All, -1]], {n, 100}] (* _Michael De Vlieger_, Jul 12 2017 *)
%o A076558 (Python)
%o A076558 from sympy import factorint
%o A076558 def a(n):
%o A076558     f=factorint(n)
%o A076558     l=[f[p] for p in f]
%o A076558     return 0 if n==1 else len(l)*min(l)
%o A076558 print([a(n) for n in range(1, 51)]) # _Indranil Ghosh_, Jul 13 2017
%o A076558 (PARI) a(n) = if(n == 1, 0, my(e = factor(n)[, 2]); vecmin(e) * #e); \\ _Amiram Eldar_, Sep 08 2024
%Y A076558 Cf. A000079, A001221, A001222, A051904, A076526.
%K A076558 easy,nonn
%O A076558 1,4
%A A076558 _Joseph L. Pe_, Nov 10 2002
%E A076558 a(1)=0 prepended by _Antti Karttunen_, Jul 12 2017