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A064491 a(1) = 1, a(n+1) = a(n) + tau(a(n)), where tau(n) (A000005) is the number of divisors of n.

%I A064491 #49 Dec 14 2021 02:06:12
%S A064491 1,2,4,7,9,12,18,24,32,38,42,50,56,64,71,73,75,81,86,90,102,110,118,
%T A064491 122,126,138,146,150,162,172,178,182,190,198,210,226,230,238,246,254,
%U A064491 258,266,274,278,282,290,298,302,306,318,326,330,346,350,362,366,374
%N A064491 a(1) = 1, a(n+1) = a(n) + tau(a(n)), where tau(n) (A000005) is the number of divisors of n.
%C A064491 a(n) = partial sums of A165930(n). [_Jaroslav Krizek_, Sep 30 2009]
%D A064491 Claudia Spiro, Problem proposed at West Coast Number Theory Meeting, 1977. [If you change the starting term, does the resulting sequence always join this one? Does the parity of terms change infinitely often?] - From _N. J. A. Sloane_, Jan 11 2013
%H A064491 T. D. Noe, <a href="/A064491/b064491.txt">Table of n, a(n) for n=1..1000</a>
%F A064491 It seems likely that there exist constants c_1 and c_2 such that c_1*n*log(n) < a(n) < c_2*n*log(n) for all sufficiently large n. - _Franklin T. Adams-Watters_, Jun 25 2008
%F A064491 a(n+1) = A062249(a(n)). - _Reinhard Zumkeller_, Mar 29 2014
%t A064491 a[n_] := a[n] = a[n - 1] + DivisorSigma[0, a[n - 1]]; a[1] = 1; Table[a[n], {n, 1, 57}] (* _Jean-François Alcover_, Oct 11 2012 *)
%t A064491 NestList[#+DivisorSigma[0,#]&,1,60] (* _Harvey P. Dale_, Feb 05 2017 *)
%o A064491 (PARI) { for (n=1, 1000, if (n>1, a+=numdiv(a), a=1); write("b064491.txt", n, " ", a) ) } \\ _Harry J. Smith_, Sep 16 2009
%o A064491 (Haskell)
%o A064491 a064491 n = a064491_list !! (n-1)
%o A064491 a064491_list = iterate a062249 1  -- _Reinhard Zumkeller_, Mar 29 2014
%o A064491 (Python)
%o A064491 from itertools import islice
%o A064491 from sympy import divisor_count
%o A064491 def A064491gen(): # generator of terms
%o A064491     n = 1
%o A064491     yield n
%o A064491     while True:
%o A064491         n += divisor_count(n)
%o A064491         yield n
%o A064491 A064491_list = list(islice(A064491gen(),20)) # _Chai Wah Wu_, Dec 13 2021
%Y A064491 Cf. A000005, A165930, A165494, A165495, A165496, A165497, A165498, A165499.
%K A064491 nice,nonn
%O A064491 1,2
%A A064491 Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 04 2001
%E A064491 Beginning of sequence corrected by _T. D. Noe_, Sep 13 2007