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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.
21
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
OFFSET
1,2
COMMENTS
a(n) = partial sums of A165930(n). [Jaroslav Krizek, Sep 30 2009]
REFERENCES
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
FORMULA
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
a(n+1) = A062249(a(n)). - Reinhard Zumkeller, Mar 29 2014
MATHEMATICA
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 *)
PROG
(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)
a064491_list = iterate a062249 1 -- Reinhard Zumkeller, Mar 29 2014
(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
A064491_list = list(islice(A064491gen(), 20)) # Chai Wah Wu, Dec 13 2021
KEYWORD
nice,nonn
AUTHOR
Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 04 2001
EXTENSIONS
Beginning of sequence corrected by T. D. Noe, Sep 13 2007
STATUS
approved