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A048106
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Number of unitary divisors of n (A034444) - number of non-unitary divisors of n (A048105).
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6
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1, 2, 2, 1, 2, 4, 2, 0, 1, 4, 2, 2, 2, 4, 4, -1, 2, 2, 2, 2, 4, 4, 2, 0, 1, 4, 0, 2, 2, 8, 2, -2, 4, 4, 4, -1, 2, 4, 4, 0, 2, 8, 2, 2, 2, 4, 2, -2, 1, 2, 4, 2, 2, 0, 4, 0, 4, 4, 2, 4, 2, 4, 2, -3, 4, 8, 2, 2, 4, 8, 2, -4, 2, 4, 2, 2, 4, 8, 2, -2, -1, 4, 2, 4, 4, 4, 4, 0, 2, 4, 4, 2, 4, 4, 4, -4, 2, 2, 2
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OFFSET
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1,2
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LINKS
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FORMULA
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Dirichlet g.f: zeta(s)^2*(2/zeta(2*s) - 1).
Sum_{k=1..n} a(k) ~ (12/Pi^2 - 1)*n*log(n) + ((12/Pi^2-1)*(2*gamma-1) - (24/Pi^2)*zeta'(2)/zeta(2))*n, where gamma is Euler's constant (A001620). (End)
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MATHEMATICA
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Table[2^(1 + PrimeNu@ n) - DivisorSigma[0, n], {n, 99}] (* Michael De Vlieger, Aug 01 2017 *)
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PROG
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(Python)
from sympy import divisor_count, primefactors
def a(n): return 1 if n==1 else 2**(1 + len(primefactors(n))) - divisor_count(n) # Indranil Ghosh, May 25 2017
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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