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
Jorma K. Merikoski, Pentti Haukkanen, and Timo Tossavainen, The congruence x^n = -a^n (mod m): Solvability and related OEIS sequences, Notes. Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 516-529. See p. 521.
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
KEYWORD
nonn
AUTHOR
Thomas Ordowski, Oct 07 2015
EXTENSIONS
More terms from Altug Alkan, Oct 07 2015
STATUS
approved