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A262998 Composite numbers n such that Sum_{k=1..phi(n)} k^phi(n) == phi(n) (mod n), where phi(n) = A000010(n). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Robert Israel, Table of n, a(n) for n = 1..5000

FORMULA

{2 * A002144} U {320, 480, 22113, 44226, 66339, ?}.

EXAMPLE

For a(1) = 10; phi(10) = 4, 1^4 + 2^4 + 3^4 + 4^4 = 354 == 4 (mod 10).

MAPLE

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:

select(filter, [$2..2000]); # Robert Israel, Oct 07 2015

MATHEMATICA

Select[Range[2, 3000], !PrimeQ[#] && (p= EulerPhi@ #; Mod[ Sum[ PowerMod[k, p, #], {k, p}]-p, #] == 0) &] (* Giovanni Resta, Oct 07 2015 *)

PROG

(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

CROSSREFS

Cf. A007850 (see Jonathan Sondow's comment, Jan 03 2014).

Sequence in context: A005278 A339977 A157075 * A245021 A045039 A322972

Adjacent sequences:  A262995 A262996 A262997 * A262999 A263000 A263001

KEYWORD

nonn

AUTHOR

Thomas Ordowski, Oct 07 2015

EXTENSIONS

More terms from Altug Alkan, Oct 07 2015

STATUS

approved

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Last modified January 18 03:02 EST 2022. Contains 350410 sequences. (Running on oeis4.)