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A113808
Positive integers n such that S(n) divides n, where S(n) is the sum of the iterates of the Euler phi-function of n, that is, S(n) = phi(n)+phi(phi(n))+....+ 1.
1
1, 2, 3, 6, 9, 15, 18, 27, 30, 39, 54, 78, 81, 111, 162, 183, 222, 243, 255, 327, 363, 366, 471, 486, 510, 654, 726, 729, 942, 1458, 2187, 2199, 3063, 4359, 4374, 4375, 4398, 5571, 6126, 6561, 8718, 8750, 8751, 11142, 13122, 15723, 17502, 19683, 31446, 36759
OFFSET
1,2
LINKS
Igor E. Shparlinski, On the sum of iterations of the Euler function, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.6.
EXAMPLE
18 is in the sequence because phi(18)+phi(phi(18))+phi(phi(phi(18))) = 6 + 2 + 1 = 9, which divides 18.
MATHEMATICA
s[1]=1; s[n_] := Total@NestWhileList[EulerPhi, n, #>1 &] - n; Select[Range@ 1000, Mod[#, s@#] == 0 &] (* Giovanni Resta, May 25 2013 *)
PROG
(PARI) lista(nn) = {for (n=1, nn, s = 0; m = n; until (m == 1, m = eulerphi(m); s += m; ); if ((n % s == 0), print1(n, ", ")); ); } \\ Michel Marcus, May 25 2013
CROSSREFS
Sequence in context: A200273 A303664 A190276 * A337114 A308870 A273371
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Jan 22 2006
STATUS
approved