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A274468
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The length of the initial uninterrupted number of tau numbers in the chain defined by repeated subtraction of the number of divisors, starting with the n-th tau number.
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3
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1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 3, 2, 4, 5, 5, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 3, 1, 2, 1, 1, 1, 1, 1
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OFFSET
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1,6
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COMMENTS
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This is the persistence of the n-th tau number staying a tau number under the map x->A049820(x).
Records: 1, 2,...,8 occur at n=1, 6, 14, 16, 17, 7393, 7394, 8064,...
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LINKS
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EXAMPLE
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a(196)=4 because the 196th tau number is 2016. Subtracting tau(2016)=36 gives 1980, which is a tau number. Subtracting tau(1980)=36 gives 1944, which is a tau number. Subtracting tau(1944)=24 gives 1920, which is a tau number. Subtracting tau(1920)=32 gives 1888 which is not a tau number. The length of the chain 2016->1980->1944->1920 is 4.
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MAPLE
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isA033950 := proc(n)
if n <= 0 then
false;
elif n = 1 then
true;
else
modp(n, numtheory[tau](n)) = 0 ;
end if;
end proc:
option remember;
local a, t ;
a := 1 ;
while true do
if isA033950(t) then
a := a+1 ;
else
break;
end if;
end do:
a ;
end proc:
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MATHEMATICA
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isA033950[n_] := Which[n <= 0, False, n == 1, True, True, IntegerQ[ n/DivisorSigma[0, n]]];
A033950[n_] := A033950[n] = Module[{k}, If[n == 1, 1, For[k = A033950[n-1] + 1, True, k++, If[IntegerQ[k/DivisorSigma[0, k]], Return[k]]]]];
A274468[n_] := A274468[n] = Module[{a, t}, t = A033950[n]; a = 1; While[ True, t = t-DivisorSigma[0, t]; If[isA033950[t], a++, Break[]]]; a];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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