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

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

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

Cf. A000005, A165930, A165494, A165495, A165496, A165497, A165498, A165499.

Sequence in context: A186357 A212988 A344290 * A120878 A137996 A360627

Adjacent sequences: A064488 A064489 A064490 * A064492 A064493 A064494

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