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%I #15 Oct 11 2017 05:18:09
%S 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,
%T 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,
%U 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
%N Number of divisors d of number n such that sigma(d) does not divide n.
%C Sigma(n) = A000203(n). a(n) = A000005(n) - A173441(n).
%C a(n) >= 1 for n >= 2, with equality if and only if n is prime. - _Robert Israel_, Oct 10 2017
%H Robert Israel, <a href="/A173442/b173442.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%p f:= n -> nops(select(t -> n mod numtheory:-sigma(t) <> 0, numtheory:-divisors(n))):
%p map(f, [$1..100]); # _Robert Israel_, Oct 10 2017
%t Table[Length[Select[Divisors[n], Not[Divisible[n, DivisorSigma[1, #]]], &]], {n, 100}] (* _Alonso del Arte_, Oct 10 2017 *)
%o (PARI) a(n) = sumdiv(n, d, (n % sigma(d)) != 0); \\ _Michel Marcus_, Oct 11 2017
%Y Cf. A000005, A000203, A173441.
%K nonn
%O 1,4
%A _Jaroslav Krizek_, Feb 18 2010
%E More terms from _Robert Israel_, Oct 10 2017
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