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
LINKS
T. D. Noe, Table of n, a(n) for n=1..1000
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
CROSSREFS
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