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%I #20 May 25 2017 22:06:15
%S 1,2,1,2,1,3,1,3,2,3,1,6,1,3,1,3,1,5,1,4,1,3,1,8,1,3,2,4,1,4,1,3,1,3,
%T 1,9,1,3,1,6,1,4,1,4,2,3,1,8,1,3,1,4,1,5,1,6,1,3,1,11,1,3,2,3,1,4,1,4,
%U 1,4,1,12,1,3,2,4,1,4,1,8,2,3,1,11,1,3,1,6,1,7,1,4,1,3,1,10,1,3,2,4,1,4,1,6
%N a(n) = number of positive divisors, k, of n where d(k) divides n (where d(k) = number of positive divisors of k, A000005).
%C First occurrence of k: 1, 2, 6, 20, 18, 12, 90, 24, 36, 96, 60, 72, 5670, 972, 120, 336, 180, 420, 540, 240, 600, 2352, 360, 480, 900, 3000, 840, 1080, 1260, 720, ..., . - _Robert G. Wilson v_
%H Antti Karttunen, <a href="/A138012/b138012.txt">Table of n, a(n) for n = 1..10000</a>
%e 10 has 4 divisors (1,2,5,10). The number of divisors of each of these divisors of 10 form the sequence (1,2,2,4). Of these, three divide 10: 1,2,2. So a(10) = 3.
%p with(numtheory): a:=proc(n) local div, ct, j: div:=divisors(n): ct:=0: for j to tau(n) do if `mod`(n, tau(div[j]))=0 then ct:=ct+1 else end if end do: ct end proc: seq(a(n),n=1..80); # _Emeric Deutsch_, Mar 14 2008
%t Table[Length[Select[Divisors[n], Mod[n, Length[Divisors[ # ]]] == 0 &]], {n,1,100}] (* _Stefan Steinerberger_ *)
%t f[n_] := Count[Mod[n, DivisorSigma[0, Divisors@n]], 0]; Array[f, 104] (* _Robert G. Wilson v_ *)
%o (PARI) A138012(n) = sumdiv(n,d,if(!(n%numdiv(d)), 1, 0)); \\ _Antti Karttunen_, May 25 2017
%o (Python)
%o from sympy import divisors, divisor_count
%o def a(n): return sum([1*(n%divisor_count(d)==0) for d in divisors(n)]) # _Indranil Ghosh_, May 25 2017
%Y Cf. A000005, A138010, A138011.
%K nonn
%O 1,2
%A _Leroy Quet_, Feb 27 2008
%E More terms from _Stefan Steinerberger_ and _Robert G. Wilson v_, Feb 29 2008
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