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%I #22 May 05 2020 07:18:00
%S 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 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 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 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 Omega(n) >= a(n) for n >= 1, where Omega(n) = the number of prime factors of n, counting multiplicity.
%C Positions of records are A000079. - _David A. Corneth_, May 05 2020
%H Antti Karttunen, <a href="/A076558/b076558.txt">Table of n, a(n) for n = 1..10000</a>
%H 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 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F a(n) = A001221(n) * A051904(n). - _Antti Karttunen_, Jul 12 2017
%t a[n_] := Module[{pf}, pf = Transpose[FactorInteger[n]]; Length[pf[[1]]]*Min[pf[[2]]]]; Table[a[i] - Boole[i == 1], {i, 100}]
%t (* Second program: *)
%t Table[Length[#] Min[#] - Boole[n == 1] &@ FactorInteger[n][[All, -1]], {n, 100}] (* _Michael De Vlieger_, Jul 12 2017 *)
%o (Python)
%o from sympy import factorint
%o def a(n):
%o f=factorint(n)
%o l=[f[p] for p in f]
%o return 0 if n==1 else len(l)*min(l)
%o print([a(n) for n in range(1, 51)]) # _Indranil Ghosh_, Jul 13 2017
%Y Cf. A000079, A001221, A051904, A076526.
%K easy,nonn
%O 1,4
%A _Joseph L. Pe_, Nov 10 2002
%E a(1)=0 prepended by _Antti Karttunen_, Jul 12 2017
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