OFFSET
1,10
COMMENTS
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
LINKS
FORMULA
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
EXAMPLE
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.
MAPLE
seq(6 &^ (6^6) mod n, n=1..100); # Robert Israel, Nov 27 2019
MATHEMATICA
Table[PowerMod[6, 6^6, n], {n, 100}]
PROG
(PARI) a(n)=lift(Mod(6, n)^6^6) \\ Charles R Greathouse IV, Jul 05 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Marvin Ray Burns, Jul 04 2012
STATUS
approved