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a(1)=1. For n>1, a(n) = the smallest positive multiple of n such that phi(a(n)) >= phi(a(n-1)), where phi(m) is A000010(m).
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%I #25 Sep 22 2015 08:40:01

%S 1,2,3,4,5,12,7,16,27,50,33,72,39,56,45,64,51,108,57,100,105,154,115,

%T 288,125,286,243,392,203,690,217,416,363,544,455,864,407,836,663,1000,

%U 451,1512,559,1276,1125,1334,799,2256,931,2000,1377,1924,1007,2862,1375

%N a(1)=1. For n>1, a(n) = the smallest positive multiple of n such that phi(a(n)) >= phi(a(n-1)), where phi(m) is A000010(m).

%C A143483(n) = phi(a(n)).

%C A143480 is an analogous sequence but with phi(a(n)) > phi(a(n-1)).

%H Peter Kagey, <a href="/A143482/b143482.txt">Table of n, a(n) for n = 1..10000</a>

%e a(9) = 27 because:

%e phi(9) = 6 < 8 = phi(a(8)),

%e phi(18) = 6 < 8 = phi(a(8)),

%e phi(27) = 18 >= 8 = phi(a(8)).

%t a = t = {1}; lim = 55; Do[k = 1; While[EulerPhi[k n] < t[[n - 1]], k++]; AppendTo[a, k n]; AppendTo[t, EulerPhi[k n]], {n, 2, lim}]; a (* _Michael De Vlieger_, Sep 04 2015 *)

%o (PARI) lista(nn) = {print1(a=1, ", "); for (n=2, nn, k = 1; phia = eulerphi(a); while(eulerphi(k*n) < phia, k++); a = k*n; print1(a, ", "););} \\ _Michel Marcus_, Sep 22 2015

%Y Cf. A000010, A143480, A143483.

%K nonn

%O 1,2

%A _Leroy Quet_, Aug 19 2008

%E Extended by _Ray Chandler_, Nov 09 2008