A357125 -id:A357125 - cp's OEIS frontend

A245319 Numbers k that divide 2^k + 8.

1, 2, 4, 5, 6, 8, 12, 18, 24, 36, 72, 88, 198, 228, 1032, 2412, 2838, 4553, 5958, 10008, 24588, 25938, 46777, 65538, 75468, 82505, 130056, 143916, 200364, 540738, 598818, 750852, 797478, 923628, 958212, 1151538, 1250568, 1505388, 1647396, 2365128, 2964036, 3490028, 3704418, 3844808

Offset: 1

Derek Orr, Jul 17 2014

nonn

			2^4 + 8 = 24 is divisible by 4. Thus 4 is a term of this sequence.
2^5 + 8 = 40 is divisible by 5. Thus 5 is a term of this sequence.

Chai Wah Wu, Table of n, a(n) for n = 1..929 (terms 1..58 from Harvey P. Dale)
OEIS Wiki, 2^n mod n

The odd terms form A357125.

Cf. A015922.

select(n -> 2 &^ n + 8 mod n = 0, [$1..10^6]); # Robert Israel, Jul 18 2014

Join[Select[Range[7],Divisible[2^#+8,#]&],Select[Range[4000000], Abs[ PowerMod[ 2,#,#]-#]==8&]] (* Harvey P. Dale, May 25 2016 *)

for(n=1,10^9,if(Mod(2,n)^n==Mod(-8,n),print1(n,", ")));

A251603 Numbers k such that k + 2 divides k^k - 2.

Original entry on oeis.org

3, 4551, 46775, 82503, 106976, 1642796, 4290771, 4492203, 4976427, 21537831, 21549347, 21879936, 51127259, 56786087, 60296571, 80837771, 87761787, 94424463, 96593696, 138644871, 168864999, 221395539, 255881451, 297460451, 305198247, 360306363, 562654203

Offset: 1

Juri-Stepan Gerasimov, Dec 05 2014

nonn

Numbers k such that (k^k - 2)/(k + 2) is an integer.
Since k == -2 (mod k+2), also numbers k such that k + 2 divides (-2)^k - 2. - Robert Israel, Jan 04 2015
Numbers k == 0 (mod 4) such that A066602(k/2+1) = 8, and odd numbers k such that k = 3 or A082493(k+2) = 8. - Robert Israel, Apr 08 2015

			3 is in this sequence because 3 + 2 = 5 divides 3^3 - 2 = 25.

Max Alekseyev, Table of n, a(n) for n = 1..890 (all terms below 10^15)

Cf. A001477, A004273, A004275, A066602, A082493, A081765, A213382, A252606, A357125.

[n: n in [0..10000] | Denominator((n^n-2)/(n+2)) eq 1];

isA251603 := proc(n)
    if modp(n &^ n-2,n+2) = 0 then
        true;
    else
        false;
    end if;
end proc:
A251603 := proc(n)
    option remember;
    local a;
    if n = 1 then
        3;
    else
        for a from procname(n-1)+1 do
            if isA251603(a) then
                return a;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Jan 09 2015

Select[Range[10^6], Mod[PowerMod[#, #, # + 2] - 2, # + 2] == 0 &] (* Michael De Vlieger, Dec 20 2014, based on Robert G. Wilson v at A252041 *)

for(n=1,10^9,if(Mod(n,n+2)^n==+2,print1(n,", "))); \\ Joerg Arndt, Dec 06 2014

A251603_list = [n for n in range(1,10**6) if pow(n, n, n+2) == 2] # Chai Wah Wu, Apr 13 2015

The even terms form A122711, the odd terms are those in A245319 (forming A357125) decreased by 2. - Max Alekseyev, Sep 22 2016

a(6)-a(27) from Joerg Arndt, Dec 06 2014

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A245319 Numbers k that divide 2^k + 8.

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A251603 Numbers k such that k + 2 divides k^k - 2.

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