A340317 (Product of primes <= n) read modulo n.

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, 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, 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

Offset

1,4

Comments

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

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).

Links

Table of n, a(n) for n=1..99.

Formula

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

Example

n = 1; a(1) = 1 mod 1 = 0;
n = 2; a(2) = 2 mod 2 = 0;
n = 3; a(3) = 2*3 mod 3 = 0;
n = 4; a(4) = 2*3 mod 4 = 2;
n = 5; a(5) = 2*3*5 mod 5 = 0;
n = 6; a(6) = 2*3*5 mod 6 = 0;
and so on.

Prog

(PARI) a(n) = lcm(primes([2, n])) % n; \\ Michel Marcus, Jan 07 2021

Crossrefs

Cf. A005117, A013929, A034386.

Sequence in context: A063958 A349434 A126164 * A145007 A308376 A228616

Adjacent sequences: A340314 A340315 A340316 * A340318 A340319 A340320

Keyword

nonn

Author

Ctibor O. Zizka, Jan 04 2021

Status

approved