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%I #52 Nov 28 2015 13:21:39
%S 10,26,34,58,74,82,106,122,146,178,194,202,218,226,274,298,314,320,
%T 346,362,386,394,458,466,480,482,514,538,554,562,586,626,634,674,698,
%U 706,746,778,794,802,818,842,866,898,914,922,1018,1042,1082,1114,1138,1154,1186,1202,1226,1234,1282,1306
%N Composite numbers n such that Sum_{k=1..phi(n)} k^phi(n) == phi(n) (mod n), where phi(n) = A000010(n).
%C The terms a(18) = 320 and a(25) = 480 are not of the form 2p, where prime p == 1 (mod 4). - _Altug Alkan_, Oct 07 2015
%C The term a(662) = 22113 is the first odd term and the third one not of the form above. - _Giovanni Resta_, Oct 07 2015
%C If n == 1 (mod 4) is in the sequence, then so is 2n. - _Thomas Ordowski_, Oct 07 2015
%H Robert Israel, <a href="/A262998/b262998.txt">Table of n, a(n) for n = 1..5000</a>
%F {2 * A002144} U {320, 480, 22113, 44226, 66339, ?}.
%e For a(1) = 10; phi(10) = 4, 1^4 + 2^4 + 3^4 + 4^4 = 354 == 4 (mod 10).
%p filter:= proc(n) local p;
%p if isprime(n) then return false fi;
%p p:= numtheory:-phi(n);
%p evalb(add(i &^ p mod n, i=1..p) mod n = p)
%p end proc:
%p select(filter, [$2..2000]); # _Robert Israel_, Oct 07 2015
%t Select[Range[2, 3000], !PrimeQ[#] && (p= EulerPhi@ #; Mod[ Sum[ PowerMod[k, p, #], {k, p}]-p, #] == 0) &] (* _Giovanni Resta_, Oct 07 2015 *)
%o (PARI) forcomposite(n=1, 3000, if(lift(sum(k=1,eulerphi(n), Mod(k, n)^eulerphi(n))) == eulerphi(n), print1(n", "))); \\ _Altug Alkan_, Oct 07 2015
%Y Cf. A007850 (see Jonathan Sondow's comment, Jan 03 2014).
%K nonn
%O 1,1
%A _Thomas Ordowski_, Oct 07 2015
%E More terms from _Altug Alkan_, Oct 07 2015
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