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A076558
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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.
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3
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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, 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, 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
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OFFSET
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1,4
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COMMENTS
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Omega(n) >= a(n) for n >= 1, where Omega(n) = the number of prime factors of n, counting multiplicity.
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LINKS
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FORMULA
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MATHEMATICA
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a[n_] := Module[{pf}, pf = Transpose[FactorInteger[n]]; Length[pf[[1]]]*Min[pf[[2]]]]; Table[a[i] - Boole[i == 1], {i, 100}]
(* Second program: *)
Table[Length[#] Min[#] - Boole[n == 1] &@ FactorInteger[n][[All, -1]], {n, 100}] (* Michael De Vlieger, Jul 12 2017 *)
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PROG
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(Python)
from sympy import factorint
def a(n):
f=factorint(n)
l=[f[p] for p in f]
return 0 if n==1 else len(l)*min(l)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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