# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a006874 Showing 1-1 of 1 %I A006874 M0535 #57 Nov 15 2023 11:52:07 %S A006874 1,1,2,3,4,6,6,9,10,12,10,22,12,18,24,27,16,38,18,44,36,30,22,78,36, %T A006874 36,50,66,28,104,30,81,60,48,72,158,36,54,72,156,40,156,42,110,152,66, %U A006874 46,270,78,140,96,132,52,230,120,234,108,84,58,456,60,90,228,243,144,260 %N A006874 Number of mu-atoms of period n on continent of Mandelbrot set. %D A006874 B. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, NY, 1982, p. 183. %D A006874 R. Penrose, The Emperor's New Mind, Penguin Books, NY, 1991, p. 138. %D A006874 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A006874 Vincenzo Librandi, Table of n, a(n) for n = 1..10000 %H A006874 R. P. Munafo, Mu-Ency - The Encyclopedia of the Mandelbrot Set %H A006874 F. V. Weinstein, Notes on Fibonacci partitions, arXiv:math/0307150 [math.NT], 2003-2018. %F A006874 a(n) = Sum_{ d divides n, d1, a(1)=1, where phi is Euler totient function (A000010). - _Vladeta Jovovic_, Feb 09 2002 %F A006874 a(1)=1; for n > 1, a(n) = Sum_{k=1..n-1} a(gcd(n,k)). - _Reinhard Zumkeller_, Sep 25 2009 %F A006874 G.f. A(x) satisfies: A(x) = x + Sum_{k>=2} phi(k) * A(x^k). - _Ilya Gutkovskiy_, Sep 04 2019 %e A006874 a(1) = 1; %e A006874 a(2) = a(1); %e A006874 a(3) = 2*a(1); %e A006874 a(4) = 2*a(1) + a(2); %e A006874 a(5) = 4*a(1); %e A006874 a(6) = 2*a(1) + 2*a(2) + a(3); %e A006874 a(7) = 6*a(1); %e A006874 a(8) = 4*a(1) + 2*a(2) + a(4); %e A006874 a(9) = 6*a(1) + 2*a(3); %e A006874 a(10) = 4*a(1) + 4*a(2) + a(5); %e A006874 a(11) = 10*a(1); %e A006874 a(12) = 4*a(1) + 2*a(2) + 2*a(3) + 2*a(4) + a(6); ... %t A006874 a[1] = 1; a[n_] := a[n] = Block[{d = Most@Divisors@n}, Plus @@ (EulerPhi[n/d]*a /@ d)]; Array[a, 66] (* _Robert G. Wilson v_, Nov 22 2005 *) %o A006874 (PARI) a(n) = if (n==1, 1, sumdiv(n, d, if (d==1, 0, a(n/d)*eulerphi(d)))); \\ _Michel Marcus_, Apr 19 2014 %o A006874 (Python) %o A006874 from sympy import divisors, totient %o A006874 l=[0, 1] %o A006874 for n in range(2, 101): %o A006874 l.append(sum([totient(n//d)*l[d] for d in divisors(n)[:-1]])) %o A006874 print(l[1:]) # _Indranil Ghosh_, Jul 12 2017 %o A006874 (Magma) sol:=[1]; for n in [2..66] do Append(~sol,&+[sol[Gcd(n,k)]:k in [1..n-1]]); end for; sol; // _Marius A. Burtea_, Sep 05 2019 %Y A006874 Cf. A000010, A006875, A006876. %K A006874 nonn %O A006874 1,3 %A A006874 _Robert Munafo_, Apr 28 1994 %E A006874 More terms from _Vladeta Jovovic_, Feb 09 2002 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE