A089090 -id:A089090 - cp's OEIS frontend

A204919 a(n) = q^2 where q is the least prime such that n divides A204916(n)^2 - q^2.

4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 49, 4, 9, 4, 25, 289, 25, 4, 49, 4, 9, 4, 49, 4, 25, 4, 121, 9, 49, 961, 49, 4, 9, 4, 121, 4, 25, 4, 289, 1681, 25, 4, 361, 4, 49, 2209, 529, 4, 9, 4, 289, 4, 49

Offset: 1

Clark Kimberling, Jan 20 2012

nonn

For a guide to related sequences, see A204892.

Original name was "Least prime q^2 such that n divides p^2-q^2 for some prime p>q", which would be A089090. - Robert Israel, May 04 2019

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A089090, A204916, A204908, A204900, A204892.

N:= 100: # to get a(1)..a(N)
A:= Vector(N): count:= 0:
p:= 2: P:= 2:
for i from 1 while count < N do
  p:= nextprime(p);
  ps:= p^2;
  P:= P, p;
  for j from 1 to i while count < N do
   qs:= P[j]^2;
   S:= convert(select(t -> t <= N and A[t]=0, numtheory:-divisors(ps-qs)),list);
   A[S]:= qs;
   count:= count + nops(S);
od od:
convert(A,list); # Robert Israel, May 04 2019

Mathematica
```
(See the program at A204916.)
```

Name corrected by Robert Israel, May 04 2019

A126601 a(n) = n-th composite from among those composites which are coprime to n.

Original entry on oeis.org

4, 15, 10, 25, 12, 77, 15, 39, 26, 69, 20, 121, 22, 81, 56, 69, 27, 161, 30, 121, 65, 105, 35, 205, 49, 119, 68, 141, 44, 391, 46, 123, 92, 141, 81, 287, 54, 153, 106, 213, 58, 425, 62, 185, 146, 177, 66, 343, 82, 259, 128, 209, 75, 385, 114, 253, 142, 215, 82, 671, 85

Offset: 1

Leroy Quet, Jan 06 2007

nonn

			The composites which are coprime to 6 are: 25,35,49,55,65,77,85,...So a(6) is the 6th of these, which is 77.

Michel Marcus, Table of n, a(n) for n = 1..1000

Cf. A089090 (the 1st such composite).

f[n_] := Block[{k = 1, c = n},While[c > 0,k++;While[PrimeQ[k] || GCD[k, n] > 1, k++ ];c--;];k];Table[f[n], {n, 61}] (* Ray Chandler, Jan 08 2007 *)

a(n) = {my(c=2, nb=0); while(nb != n, c++; if (!isprime(c) && (gcd(c,n)==1), nb++)); c;} \\ Michel Marcus, Sep 06 2019

Extended by Ray Chandler, Jan 08 2007

cp's OEIS Frontend

A204919 a(n) = q^2 where q is the least prime such that n divides A204916(n)^2 - q^2.

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