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A340354 a(n) is the sum, for j < n coprime to n, of the least prime > n congruent to j (mod n).

%I A340354 #12 Jan 06 2021 08:30:02
%S A340354 3,12,12,50,18,112,64,126,60,330,72,520,182,240,240,884,198,1368,320,
%T A340354 588,462,1886,360,1650,676,1296,644,3074,390,4030,1248,1848,1292,2380,
%U A340354 864,5328,1596,2496,1280,6560,840,7740,2112,2880,2530,9588,1632,7938,2250,4896,3224,12402,1890,6820,2968
%N A340354 a(n) is the sum, for j < n coprime to n, of the least prime > n congruent to j (mod n).
%C A340354 For each n >= 3, a(n) is divisible by n.
%H A340354 Robert Israel, <a href="/A340354/b340354.txt">Table of n, a(n) for n = 2..3000</a>
%e A340354 For n=6 the primes are 7 == 1 (mod 6) and 11 == 5 (mod 6), so a(6) = 7+11=18.
%p A340354 f:= proc(n) local t, k,p;
%p A340354   t:= 0:
%p A340354   for k from 1 to n-1 do
%p A340354    if igcd(k,n) = 1 then
%p A340354      for p from n+k by n do
%p A340354        if isprime(p) then
%p A340354          t:= t+p;
%p A340354          break
%p A340354        fi
%p A340354      od
%p A340354    fi
%p A340354   od;
%p A340354   t
%p A340354 end proc:
%p A340354 map(f, [$2..100]);
%Y A340354 Row sums of A060940 (starting with second row).
%K A340354 nonn,look
%O A340354 2,1
%A A340354 _J. M. Bergot_ and _Robert Israel_, Jan 05 2021