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A064491
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a(1) = 1, a(n+1) = a(n) + tau(a(n)), where tau(n) (A000005) is the number of divisors of n.
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21
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1, 2, 4, 7, 9, 12, 18, 24, 32, 38, 42, 50, 56, 64, 71, 73, 75, 81, 86, 90, 102, 110, 118, 122, 126, 138, 146, 150, 162, 172, 178, 182, 190, 198, 210, 226, 230, 238, 246, 254, 258, 266, 274, 278, 282, 290, 298, 302, 306, 318, 326, 330, 346, 350, 362, 366, 374
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listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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REFERENCES
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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
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
NestList[#+DivisorSigma[0, #]&, 1, 60] (* Harvey P. Dale, Feb 05 2017 *)
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PROG
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(PARI) { for (n=1, 1000, if (n>1, a+=numdiv(a), a=1); write("b064491.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 16 2009
(Haskell)
a064491 n = a064491_list !! (n-1)
(Python)
from itertools import islice
from sympy import divisor_count
def A064491gen(): # generator of terms
n = 1
yield n
while True:
n += divisor_count(n)
yield n
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CROSSREFS
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KEYWORD
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nice,nonn
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AUTHOR
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Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 04 2001
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EXTENSIONS
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Beginning of sequence corrected by T. D. Noe, Sep 13 2007
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STATUS
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approved
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