A129810 -id:A129810 - cp's OEIS frontend

0, 0, 0, 0, 1, 0, 1, 0, 0, 6, 5, 0, 1, 8, 6, 0, 1, 0, 1, 16, 15, 16, 2, 0, 6, 14, 0, 8, 23, 6, 1, 0, 27, 18, 1, 0, 1, 20, 27, 16, 18, 36, 1, 16, 36, 2, 37, 0, 43, 6, 18, 40, 44, 0, 16, 8, 39, 52, 5, 36, 9, 32, 36, 0, 1, 60, 14, 52, 48, 36, 6, 0, 1, 38, 6, 20, 71

Offset: 1

Marvin Ray Burns, Jul 04 2012

nonn

The indices of zeros in this sequence, i.e., divisors of 6^(6^6), are all numbers of the form 2^i * 3^j, with 0 <= i, j <= 6^6. [Edited by M. F. Hasler, Feb 25 2018]
If c and N are any positive integers, and p^k is the largest prime power divisor of c, then the divisors of c^N less than p^(k*N+1) are precisely those numbers in that range whose prime factorization includes only primes that divide c. This is the case c = 6, N = 6^6, so p^k = 2^1 = 2; so the first difference in the divisor list from A003586 is for A003586(n) = 2^(6^6+1). Franklin T. Adams-Watters, Jul 12 2012
Eventually constant: see formula. - M. F. Hasler, Feb 24 2018
If n > 1 is coprime to 6 and A000010(n) divides 6^6 then a(n)=1. - Robert Israel, Nov 27 2019

			a(1) = 6^(6^6) mod 1 = 0.
a(2) = 6^(6^6) mod 2 = 0.
a(3) = 6^(6^6) mod 3 = 0.
a(4) = 6^(6^6) mod 4 = 0.

Robert Israel, Table of n, a(n) for n = 1..10000
Index entries for eventually constant sequences.

Cf. A129810 (9^9^9 mod n), A003586.

seq(6 &^ (6^6) mod n, n=1..100); # Robert Israel, Nov 27 2019

Mathematica
```
Table[PowerMod[6, 6^6, n], {n, 100}]
```

a(n)=lift(Mod(6,n)^6^6) \\ Charles R Greathouse IV, Jul 05 2012

a(n) = 0 if and only if n = 2^i 3^j, 0 <= i, j <= 6^6; after the last of these zeros at n = 6^6^6, a(n) = 6^6^6 for all n > 6^6^6 ~ 2.659*10^36305. - M. F. Hasler, Feb 24 2018

cp's OEIS Frontend

A214128 a(n) = 6^(6^6) mod n.

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