A309525 a(n) is the greatest divisor of A006190(n) that is coprime to A006190(m) for all positive integers m < n.

1, 3, 10, 11, 109, 1, 1189, 119, 1297, 131, 141481, 59, 1543321, 1429, 3089, 14159, 183642229, 433, 2003229469, 14041, 1837837, 170039, 238367471761, 7079, 23854956949, 1854841, 2186871697, 1670761, 309400794703549, 12871, 3375045015828949, 200477279

Offset: 1

Author

Jianing Song, Aug 06 2019

Keywords

• nonn
• look

Comments

Analog of A178763 and A308949.

Examples

			A006190(12) = 467280 = 2^4 * 3^2 * 5 * 11 * 59. We have 2, 3, 5 divides A006190(6) = 360 and 11 divides A006190(3) = 11, but A006190(m) is coprime to 59 for all 1 <= m < 12, so a(12) = 59.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1930

Crossrefs

Cf. A006190, A253807.

Cf. A178763, A308949, A309526.

Programs

Maple

A6190:= proc(n) option remember; 3*procname(n-1)+procname(n-2) end proc:
A6190(0):= 0: A6190(1):= 1:
f:= proc(n) local k,i,g;
  k:= A6190(n);
  for i from 1 to n-1 do
    g:= igcd(k,A6190(i));
    while g > 1 do
      k:= k/g;
      g:= igcd(k,A6190(i));
    od;
  od;
  k
end proc:
map(f, [$1..40]); # Robert Israel, Aug 02 2024

PARI

T(n) = ([3, 1; 1, 0]^n)[2, 1]
b(n) = my(v=divisors(n)); prod(i=1, #v, T(v[i])^moebius(n/v[i]))
a(n) = if(isprime(n)&&!(13%n), 1543321, if(n!=6, b(n)/gcd(n, b(n)), 1))

Formula

a(n) = A253807(n) / gcd(A253807(n), n) if n != 6, 13.