A272650 - OEIS

%I #15 Apr 25 2019 03:57:13

%S 1,5,29,83,351,519,1291,1747,3357,6553,7501,11839,17219,19263,28199,

%T 38583,56049,49043,74771,96133,89059,132087,155209,185653,221741,

%U 260983,274803,331913,314355,348943,482091,569587,641707

%N Sum_{ i in 1..p-1, j in 1..p-1, i*j mod p = 1} i*j, where p = n-th prime.

%H Gheorghe Coserea, <a href="/A272650/b272650.txt">Table of n, a(n) for n = 1..20000</a>

%H Tsz Ho Chan, <a href="https://www.emis.de/journals/INTEGERS/papers/q2/q2.Abstract.html">Product of a number and its multiplicative inverse, moments of L-functions and exponential sums</a>, Integers, 16 (2016), #A2.

%p f:=proc(n) local p,a,b,s;

%p p:=ithprime(n); s:=0;

%p for a from 1 to p-1 do

%p for b from 1 to p-1 do

%p if (a*b mod p) = 1 then s:=s+a*b; fi;

%p od: od:

%p s; end;

%p [seq(f(n),n=1..40)];

%o (PARI) a(n) = { my(p = prime(n)); sum(i = 1, p-1, i*lift(Mod(i,p)^(-1))); }

%o vector(33, n, a(n)) \\ _Gheorghe Coserea_, May 16 2016

%K nonn

%O 1,2

%A _N. J. A. Sloane_, May 10 2016