A165495 -id:A165495 - cp's OEIS frontend

A165496 Values k: A165495(k) is odd.

1, 3, 6, 7, 10, 11, 13, 16, 24, 30, 32, 40, 55, 61, 62, 91, 115, 129, 139, 190, 218, 325, 330, 344, 359, 412, 499, 709, 762, 779, 791, 1392, 2230, 2440, 2947, 3355, 6008, 6124, 6718, 6899, 7563, 7872, 8070, 12529, 15204, 17582, 19313, 20706, 28825

Offset: 1

Hugo van der Sanden, Sep 21 2009

If A064491 reaches 2(2k-1)^2, it will then start a run of odd numbers if k is in this sequence.

Cf. A064491, A165495

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

Original entry on oeis.org

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

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

a(n) = partial sums of A165930(n). [Jaroslav Krizek, Sep 30 2009]

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

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

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

a064491 n = a064491_list !! (n-1)
a064491_list = iterate a062249 1  -- Reinhard Zumkeller, Mar 29 2014

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 *)

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

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

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

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

A165494 Iterations of k -> k+tau(k) from 2(2n-1)^2 until result not divisible by 4.

Original entry on oeis.org

2, 3, 3, 3, 2, 3, 7, 2, 3, 6, 2, 9, 3, 2, 10, 3, 2, 2, 5, 7, 3, 4, 7, 10, 5, 5, 10, 8, 2, 7, 3, 8, 7, 4, 9, 36, 13, 9, 2, 6, 7, 5, 2, 2, 9, 4, 30, 2, 16, 4, 6, 6, 4, 11, 24, 16, 11, 9, 3, 11, 15, 2, 9, 10, 2, 26, 2, 10, 3, 3, 4, 13, 11, 5, 12, 3, 7, 17, 21, 17, 17, 12, 5, 4, 3, 8, 19, 9, 2

Offset: 1

Hugo van der Sanden, Sep 21 2009

This sequence and A165495 explore a critical aspect of the behavior of A064491.

			For a(2) we start at 2.3^2=18; 18+tau(18)=24; 24+tau(24)=32; 32+tau(32)=38, which is not divisible by 4, so a(2)=3 for the 3 iterations needed.

Cf. A064491, A165495

cp's OEIS Frontend

A165496 Values k: A165495(k) is odd.

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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.

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A165494 Iterations of k -> k+tau(k) from 2(2n-1)^2 until result not divisible by 4.

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