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A352420
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Number of distinct prime factors of sigma_n(n).
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1
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0, 1, 2, 3, 3, 4, 3, 2, 3, 5, 6, 8, 5, 5, 8, 6, 3, 8, 5, 11, 9, 7, 8, 10, 8, 8, 10, 12, 7, 13, 7, 11, 15, 10, 15, 11, 7, 8, 11, 10, 6, 14, 8, 14, 14, 11, 10, 17, 6, 21, 15, 16, 8, 18, 16, 15, 16, 6, 9, 22, 8, 10, 17, 13, 17, 17, 7, 17, 20, 17, 8, 23, 4, 13, 21
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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a(5) = 3; a(5) = omega(sigma_5(5)) = omega(1^5+5^5) = omega(3126) = 3.
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MAPLE
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end proc:
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MATHEMATICA
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Table[PrimeNu[DivisorSigma[n, n]], {n, 30}]
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PROG
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(PARI) a(n) = omega(sigma(n, n)); \\ Daniel Suteu, Mar 23 2022
(Python)
from sympy import primefactors, factorint
def A352420(n): return len(set().union(*(primefactors((p**((e+1)*n)-1)//(p**n-1)) for p, e in factorint(n).items()))) # Chai Wah Wu, Mar 24 2022
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CROSSREFS
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KEYWORD
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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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