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A274468 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. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
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,...
LINKS
C. Meller, Tau numbers, June 2016.
EXAMPLE
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.
MAPLE
isA033950 := proc(n)
if n <= 0 then
false;
elif n = 1 then
true;
else
modp(n, numtheory[tau](n)) = 0 ;
end if;
end proc:
A274468 := proc(n)
option remember;
local a, t ;
t := A033950(n) ;
a := 1 ;
while true do
t := A049820(t) ;
if isA033950(t) then
a := a+1 ;
else
break;
end if;
end do:
a ;
end proc:
MATHEMATICA
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];
Table[A274468[n], {n, 1, 100}] (* Jean-François Alcover, Aug 11 2023, after R. J. Mathar *)
CROSSREFS
Sequence in context: A095684 A205565 A064531 * A211993 A185646 A037829
KEYWORD
nonn
AUTHOR
R. J. Mathar, Jun 24 2016
STATUS
approved

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Last modified May 24 12:09 EDT 2024. Contains 372773 sequences. (Running on oeis4.)