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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.
3
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
OFFSET
1,4
COMMENTS
Omega(n) >= a(n) for n >= 1, where Omega(n) = the number of prime factors of n, counting multiplicity.
Positions of records are A000079. - David A. Corneth, May 05 2020
FORMULA
a(n) = A001221(n) * A051904(n). - Antti Karttunen, Jul 12 2017
MATHEMATICA
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 *)
PROG
(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)
print([a(n) for n in range(1, 51)]) # Indranil Ghosh, Jul 13 2017
(PARI) a(n) = if(n == 1, 0, my(e = factor(n)[, 2]); vecmin(e) * #e); \\ Amiram Eldar, Sep 08 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Joseph L. Pe, Nov 10 2002
EXTENSIONS
a(1)=0 prepended by Antti Karttunen, Jul 12 2017
STATUS
approved