A165743 The greatest common divisor of n and 210.

1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 1, 6, 1, 14, 15, 2, 1, 6, 1, 10, 21, 2, 1, 6, 5, 2, 3, 14, 1, 30, 1, 2, 3, 2, 35, 6, 1, 2, 3, 10, 1, 42, 1, 2, 15, 2, 1, 6, 7, 10, 3, 2, 1, 6, 5, 14, 3, 2, 1, 30, 1, 2, 21, 2, 5, 6, 1, 2, 3, 70, 1, 6, 1, 2, 15, 2, 7, 6, 1, 10, 3, 2, 1, 42, 5, 2, 3, 2, 1, 30, 7, 2, 3, 2, 5, 6

Offset: 1

Author

Mick Purcell (mickpurcell(AT)gmail.com), Sep 26 2009

Keywords

• nonn
• easy
• mult

Comments

Note: 210 = 2*3*5*7, the product of the first four primes.

gcd(n,2*3) is A089128; gcd(n,2*3*5) not currently in the OEIS. - R. J. Mathar, Feb 07 2011

Crossrefs

Cf. A089128.

Programs

Maple

seq(gcd(n, 210), n = 1 .. 100); # Emeric Deutsch, Oct 31 2009

Mathematica

a[n_] := GCD[n, 210]; Array[a, 100] (* Amiram Eldar, Sep 16 2023 *)

PARI

a(n) = gcd(n, 210); \\ Amiram Eldar, Sep 16 2023

Formula

From Amiram Eldar, Sep 16 2023: (Start)

a(n) = gcd(n, 210).

Multiplicative with a(p^e) = p if p <= 7, and 1 otherwise.

Dirichlet g.f.: zeta(s) * (1 + 1/2^s) * (1 + 2/3^s) * (1 + 4/5^s) * (1 + 6/7^s).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 117/14. (End)

Extensions

Extended by Emeric Deutsch, Oct 31 2009