A071616 - OEIS

%I #16 Jul 30 2017 21:12:34

%S 14,68,90,152,50,516,14,304,90,340,154,4008,26,308,90,608,34,2412,38,

%T 680,714,308,230,10128,50,364,594,728,174,8340,62,1984,594,68,350,

%U 7848,74,76,234,6800,246,5124,86,968,90,644,94,20256,98,1100,510,728,318

%N Smallest even number divisible by 2n which is nontotient, i.e., in A005277.

%C a(n) = 2n*A071615(n).

%H Donovan Johnson, <a href="/A071616/b071616.txt">Table of n, a(n) for n = 1..10000</a>

%e n=4: 2n=8 and number of terms in invphi(8k) is 5, 6, 10, 7, 9, 11, 3, 8, 17, 10, 6, 17, 3, 6, 17, 9, 9, 21, 0, 12, ... for k=1,2,...,20,...; zero appears first at k=19, so a(4) = 8k = 152.

%t invphi[n_, plist_] := Module[{i, p, e, pe, val}, If[plist=={}, Return[If[n==1, {1}, {}]]]; val={}; p=Last[plist]; For[e=0; pe=1, e==0||Mod[n, (p-1)pe/p]==0, e++; pe*=p, val=Join[val, pe*invphi[If[e==0, n, n*p/pe/(p-1)], Drop[plist, -1]]]]; Sort[val]]; invphi[n_] := invphi[n, Select[1+Divisors[n], PrimeQ]]; a[n_] := For[m=1, True, m++, If[invphi[2n*m]=={}, Return[2n*m]]] (* invphi[n, plist] is list of x with phi(x)=n and all prime divisors of x in plist. *)

%Y Cf. A000010, A002202, A005277, A071615.

%K nonn

%O 1,1

%A _Labos Elemer_, May 27 2002

%E Edited and extended by _Robert G. Wilson v_, May 28 2002 and by _Dean Hickerson_, Jun 04 2002