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(Product of primes <= n) read modulo n.
0

%I #24 Jan 07 2021 10:39:09

%S 0,0,0,2,0,0,0,2,3,0,0,6,0,0,0,14,0,12,0,10,0,0,0,6,20,0,24,14,0,0,0,

%T 18,0,0,0,30,0,0,0,10,0,0,0,22,15,0,0,18,28,10,0,26,0,6,0,42,0,0,0,30,

%U 0,0,21,38,0,0,0,34,0,0,0,6,0,0,45,38,0,0,0,50,33,0,0,42,0,0,0,22,0,60,0,46,0,0,0,6,0,14,33

%N (Product of primes <= n) read modulo n.

%C Empirically Sum_{i=1..n} (a(i)) < n*sqrt(n).

%C It looks like the n's, where a(n) is nonzero, are in A013929 and the n's, where a(n) = 0, are squarefree numbers (A005117).

%F For n >= 1, a(n) = A034386(n) mod n.

%e n = 1; a(1) = 1 mod 1 = 0;

%e n = 2; a(2) = 2 mod 2 = 0;

%e n = 3; a(3) = 2*3 mod 3 = 0;

%e n = 4; a(4) = 2*3 mod 4 = 2;

%e n = 5; a(5) = 2*3*5 mod 5 = 0;

%e n = 6; a(6) = 2*3*5 mod 6 = 0;

%e and so on.

%o (PARI) a(n) = lcm(primes([2, n])) % n; \\ _Michel Marcus_, Jan 07 2021

%Y Cf. A005117, A013929, A034386.

%K nonn

%O 1,4

%A _Ctibor O. Zizka_, Jan 04 2021