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A173442
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Number of divisors d of number n such that sigma(d) does not divide n.
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2
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0, 1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 2, 1, 3, 3, 4, 1, 4, 1, 5, 3, 3, 1, 4, 2, 3, 3, 4, 1, 5, 1, 5, 3, 3, 3, 5, 1, 3, 3, 7, 1, 6, 1, 5, 5, 3, 1, 6, 2, 5, 3, 5, 1, 6, 3, 4, 3, 3, 1, 7, 1, 3, 5, 6, 3, 6, 1, 5, 3, 7, 1, 8, 1, 3, 5, 5, 3, 6, 1, 9, 4, 3, 1, 6, 3, 3, 3, 7, 1, 8, 3, 5, 3, 3, 3, 8, 1, 5, 5, 8
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OFFSET
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1,4
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COMMENTS
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a(n) >= 1 for n >= 2, with equality if and only if n is prime. - Robert Israel, Oct 10 2017
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LINKS
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EXAMPLE
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For n = 12, a(12) = 2. We see that the divisors of 12 are 1, 2, 3, 4, 6, 12. The corresponding sigma(d) are 1, 3, 4, 7, 12, 28. The sigma(d) which do not divide n for 2 divisors d are 4 and 12.
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MAPLE
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f:= n -> nops(select(t -> n mod numtheory:-sigma(t) <> 0, numtheory:-divisors(n))):
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MATHEMATICA
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Table[Length[Select[Divisors[n], Not[Divisible[n, DivisorSigma[1, #]]], &]], {n, 100}] (* Alonso del Arte, Oct 10 2017 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, (n % sigma(d)) != 0); \\ Michel Marcus, Oct 11 2017
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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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