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 A007497 a(1) = 2, a(n) = sigma(a(n-1)). (Formerly M0581) 19
 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 T. D. Noe and Charles R Greathouse IV, Table of n, a(n) for n = 1..1500 (first 200 terms from 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 sigma(A007497(n-1)); fi; end; 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: A092063 A227007 A126850 * A126882 A239973 A281782 Adjacent sequences:  A007494 A007495 A007496 * A007498 A007499 A007500 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

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Last modified October 23 22:28 EDT 2019. Contains 328373 sequences. (Running on oeis4.)