%I #20 May 05 2014 14:45:30
%S 0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,
%T 0,2,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,2,0,0,
%U 0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,2
%N Exponent of 11 in prime factorization of (2^n + 3^n + 5^n + 7^n).
%C 11^a(n) is the largest power of 11 dividing (2^n + 3^n + 5^n + 7^n);
%C (2^n + 3^n + 5^n + 7^n) is divisible by 11^2 = 121 for n == 5 mod 10.
%C Among first 10000 nonzero terms there are {8182, 1652, 150, 14, 1, 1} terms with values {2, 3, 4, 5, 6, 7}, respectively.
%C Record values are a(5) = 2, a(45) = 3, a(595) = 5, a(40525) = 7, a(6482565) = 8, a(97435855) = 9, a(927694285) = 10, a(11789738455) = 11, a(129687123005) = 12, a(508958242255) = 13, a(11921425066695) = 14, a(74689992601115) = 15, a(1110371356919045) = 16, a(20886240847078255) = 17, a(229748649317860805) = 18, etc. - _Charles R Greathouse IV_, Apr 25 2014
%H Zak Seidov, <a href="/A241541/a241541.txt">Table n, a(-5 + 10*n) for n = 1..10^4.</a>
%e at n = 5, 2^n + 3^n + 5^n + 7^n = 20207 = 11^2*167,
%e at n = 15, 2^n + 3^n + 5^n + 7^n = 4778093469743 = 11^2*587*67271509.
%t Table[IntegerExponent[2^n + 3^n + 5^n + 7^n, 11], {n, 0, 100}]
%o (PARI) a(n)=valuation(2^n+3^n+5^n+7^n,11) \\ _Charles R Greathouse IV_, Apr 25 2014
%o (PARI) a(n,e=8)=my(m=11^e, o=valuation(Mod(2,m)^n +Mod(3,m)^n +Mod(5,m)^n +Mod(7,m)^n, 11)); if(o<e,o,a(n,2*e)) \\ _Charles R Greathouse IV_, Apr 25 2014
%Y Cf. A006519, A007814, A023512.
%K nonn
%O 0,6
%A _Zak Seidov_, Apr 25 2014