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

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 04 2001

Keywords

• nice
• nonn

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

Crossrefs

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

Programs

Haskell

a064491 n = a064491_list !! (n-1)
a064491_list = iterate a062249 1  -- 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 *)

PARI

{ for (n=1, 1000, if (n>1, a+=numdiv(a), a=1); write("b064491.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 16 2009

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

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

Extensions

Beginning of sequence corrected by T. D. Noe, Sep 13 2007