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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 Table of n, a(n) for n=1..95. 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 Cf. A033950, A049820. Sequence in context: A095684 A205565 A064531 * A211993 A185646 A037829 Adjacent sequences: A274465 A274466 A274467 * A274469 A274470 A274471 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.)