A084310 -id:A084310 - cp's OEIS frontend

A084309 a(n) = gcd(prime(n)-1, n).

1, 2, 1, 2, 5, 6, 1, 2, 1, 2, 1, 12, 1, 14, 1, 4, 1, 6, 1, 10, 3, 2, 1, 8, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 6, 1, 2, 1, 4, 1, 6, 1, 4, 1, 2, 1, 6, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 20, 1, 2, 9, 2, 13, 2, 1, 4, 1, 2, 1, 2, 1, 2, 3, 2, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 1, 8, 1, 6, 1, 2, 3, 2, 1, 2, 1, 2, 9, 20, 1, 2

Offset: 1

Labos Elemer, Jun 13 2003

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A084310, A084311, A084312, A084313, A084314, A084315, A084316.

A084309:=n->gcd(ithprime(n)-1,n): seq(A084309(n), n=1..150); # Wesley Ivan Hurt, Feb 01 2017

Mathematica
```
Table[GCD[Prime[w]-1, w], {w, 128}]
```

a(n) = gcd(prime(n)-1, n); \\ Michel Marcus, Feb 02 2017

A084314 a(n) = x is the smallest number such that gcd(prime(x)+1, x) = n.

Original entry on oeis.org

1, 2, 3, 4, 35, 24, 63, 56, 45, 10, 649, 132, 91, 42, 495, 48, 153, 54, 779, 700, 1785, 264, 851, 96, 1125, 286, 1647, 672, 551, 570, 341, 448, 2277, 1462, 385, 144, 1369, 418, 2145, 1000, 4797, 294, 817, 1804, 405, 414, 7003, 2016, 11515, 950, 2193, 2444

Offset: 1

Labos Elemer, Jun 13 2003

nonn

Ivan Neretin, Table of n, a(n) for n = 1..4000

Cf. A084309-A084316.

f[x_] := GCD[Prime[x]+1, x] t=Table[0, {256}]; Do[s=f[n]; If[s<257&&t[[s]]==0, t[[s]]=n], {n, 1, 100000}]; t
Module[{cc=Table[{x,GCD[Prime[x]+1,x]},{x,20000}]},Transpose[Table[ SelectFirst[ cc,#[[2]]==n&],{n,60}]][[1]]] (* Harvey P. Dale, Nov 28 2014 *)

a(n) = Min{x; A084310(x)=n}.

A180172 a(n) = gcd(prime(n)+2, n).

Original entry on oeis.org

1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 11, 3, 1, 1, 1, 1, 1, 9, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 5, 1, 1, 1, 1, 1, 9, 1, 1, 13, 5, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 5, 11, 1, 1, 1, 1, 71, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 15, 7, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1

Offset: 1

Zak Seidov, Aug 15 2010

nonn

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A003989, A052147, A084309, A084310, A180173.

[GCD(n,NthPrime(n) +2): n in [1..110]]; // G. C. Greubel, Mar 12 2023

Mathematica
```
Table[GCD[n,Prime[n]+2],{n,200}]
```

[gcd(nth_prime(n) + 2, n) for n in range(1,111)] # G. C. Greubel, Mar 12 2023

A180173 a(n) = gcd(prime(n)-2, n).

Original entry on oeis.org

1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 13, 1, 15, 1, 1, 1, 1, 1, 1, 11, 1, 3, 5, 1, 1, 7, 1, 3, 1, 1, 3, 1, 7, 1, 1, 1, 3, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 3, 1, 1, 3, 5, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 69, 1, 1, 3, 73, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3

Offset: 1

Zak Seidov, Aug 15 2010

nonn

Cf. A084309, A084310, A180172.

Mathematica
```
Table[GCD[n,Prime[n]-2],{n,200}]
```

cp's OEIS Frontend

A084309 a(n) = gcd(prime(n)-1, n).

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A084314 a(n) = x is the smallest number such that gcd(prime(x)+1, x) = n.

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A180172 a(n) = gcd(prime(n)+2, n).

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A180173 a(n) = gcd(prime(n)-2, n).

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