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A262998
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Composite numbers n such that Sum_{k=1..phi(n)} k^phi(n) == phi(n) (mod n), where phi(n) = A000010(n).
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1
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10, 26, 34, 58, 74, 82, 106, 122, 146, 178, 194, 202, 218, 226, 274, 298, 314, 320, 346, 362, 386, 394, 458, 466, 480, 482, 514, 538, 554, 562, 586, 626, 634, 674, 698, 706, 746, 778, 794, 802, 818, 842, 866, 898, 914, 922, 1018, 1042, 1082, 1114, 1138, 1154, 1186, 1202, 1226, 1234, 1282, 1306
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OFFSET
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1,1
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COMMENTS
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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
The term a(662) = 22113 is the first odd term and the third one not of the form above. - Giovanni Resta, Oct 07 2015
If n == 1 (mod 4) is in the sequence, then so is 2n. - Thomas Ordowski, Oct 07 2015
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LINKS
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FORMULA
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{2 * A002144} U {320, 480, 22113, 44226, 66339, ?}.
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EXAMPLE
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For a(1) = 10; phi(10) = 4, 1^4 + 2^4 + 3^4 + 4^4 = 354 == 4 (mod 10).
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MAPLE
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filter:= proc(n) local p;
if isprime(n) then return false fi;
p:= numtheory:-phi(n);
evalb(add(i &^ p mod n, i=1..p) mod n = p)
end proc:
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MATHEMATICA
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Select[Range[2, 3000], !PrimeQ[#] && (p= EulerPhi@ #; Mod[ Sum[ PowerMod[k, p, #], {k, p}]-p, #] == 0) &] (* Giovanni Resta, Oct 07 2015 *)
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PROG
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(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
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CROSSREFS
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Cf. A007850 (see Jonathan Sondow's comment, Jan 03 2014).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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