login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007497 a(1) = 2, a(n) = sigma(a(n-1)).
(Formerly M0581)
20
2, 3, 4, 7, 8, 15, 24, 60, 168, 480, 1512, 4800, 15748, 28672, 65528, 122880, 393192, 1098240, 4124736, 15605760, 50328576, 149873152, 371226240, 1710858240, 7926750720, 33463001088, 109760857440, 384120963072, 1468475386560, 7157589626880, 33151875434496 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Note that a(32) = 125038913126400 = 11182080^2. - Zak Seidov, Aug 29 2012
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..1500 (first 200 terms from T. D. Noe)
G. L. Cohen and H. J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 91-100.
Graeme L. Cohen, Herman J. J. te Riele, Iterating the Sum-of-Divisors Function, Experimental Mathematics, Vol. 5 (1996), No. 2, pp. 91-100.
R. G. Wilson, V, Notes, n.d.
FORMULA
Conjecture: (1/2)*log(n) < a(n+1)/a(n) < 2*log(n). - Benoit Cloitre, May 08 2003
Conjecture: a(n) == 0 mod 9 for n > 34. - Ivan N. Ianakiev, Mar 27 2014
Checked up to n = 1000. Similar statements hold for other small primes. For example, a(n) seems to be divisible by 2^22 * 3^5 * 5 * 7 = 35672555520 for all n > 99. - Charles R Greathouse IV, Mar 27 2014
MAPLE
A007497 := proc(n) options remember; if n <= 0 then RETURN(2) else numtheory[sigma](procname(n-1)); fi; end proc:
MATHEMATICA
a[1] = 2; a[n_] := a[n] = DivisorSigma[1, a[n-1]]; Table[a[n], {n, 30}]
NestList[ DivisorSigma[1, # ] &, 2, 27] (* Robert G. Wilson v, Oct 08 2010 *)
PROG
(Haskell)
a007497 n = a007497_list !! (n-1)
a007497_list = iterate a000203 2 -- Reinhard Zumkeller, Feb 27 2014
(PARI) normalize(M)={
my(P=Set(M[, 1]), f=concat(Mat(P), vector(#P))~);
for(i=1, #M~,
f[setsearch(P, M[i, 1]), 2] += M[i, 2]
);
f
};
addhelp(normalize, "normalize(M): Given a factorization matrix M, combine all like factors and order.");
sf(f)=my(v=vector(#f~, i, (f[i, 1]^(f[i, 2]+1)-1)/(f[i, 1]-1)), g=factor(v[1])~); for(i=2, #v, g=concat(g, factor(v[i])~)); normalize(g~)
v=vector(100); v[1]=2; f=factor(2); for(i=2, #v, print1(i" "); v[i]= factorback(f=sf(f))); v \\ Charles R Greathouse IV, Mar 27 2014
(Python)
from itertools import accumulate, repeat # requires Python 3.2 or higher
from sympy import divisor_sigma
A007497_list = list(accumulate(repeat(2, 100), lambda x, _: divisor_sigma(x)))
# Chai Wah Wu, May 02 2015
CROSSREFS
Cf. A000203, A175877 (positions of odd terms), A175878 (odd terms).
See also the similarly defined A051572 which has a(1) = 5 instead.
See also A257348.
Sequence in context: A227007 A370858 A126850 * A126882 A333801 A239973
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
Changed the cross-reference from the tau to the sigma-function - R. J. Mathar, Feb 17 2010
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)