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%I #38 Dec 31 2023 06:23:49
%S 1,2,1,2,1,3,1,2,1,2,1,4,1,2,1,2,1,3,1,3,1,2,1,4,1,2,1,2,1,4,1,2,1,2,
%T 1,4,1,2,1,3,1,4,1,2,1,2,1,4,1,2,1,2,1,3,1,3,1,2,1,6,1,2,1,2,1,3,1,2,
%U 1,2,1,5,1,2,1,2,1,3,1,3,1,2,1,5,1,2
%N Number of divisors d of n such that d-1 also divides n or d-1 = 0.
%C First differs from A055874 at a(20).
%H Harvey P. Dale, <a href="/A195155/b195155.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A000005(n) - A195150(n).
%F a(n) = 1 + A129308(n).
%F a(2n-1) = 1; a(2n) = 1 + A007862(n).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2. - _Amiram Eldar_, Dec 31 2023
%p with(numtheory):
%p a:= n-> add(`if`(d=1 or irem(n, d-1)=0, 1, 0), d=divisors(n)):
%p seq(a(n), n=1..200); # _Alois P. Heinz_, Oct 17 2011
%t d1[n_]:=Module[{d=Rest[Divisors[n]]},Count[d,_?(Divisible[n,#-1]&)]+1]; Array[d1, 90] (* _Harvey P. Dale_, Oct 31 2013 *)
%Y Cf. A000005, A007862, A049820, A055874, A129308, A137921, A195150, A195153.
%K nonn
%O 1,2
%A _Omar E. Pol_, Sep 19 2011
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