

A278835


Prime factors (counting multiplicity) of 10^10^10^10^2  1.


1



3, 3, 11, 17, 41, 73, 101, 137, 251, 257, 271, 353, 401, 449, 641, 751, 1201, 1409, 1601, 3541, 4001, 4801, 5051, 9091, 10753, 15361, 16001, 19841, 21001, 21401, 24001, 25601, 27961, 37501, 40961, 43201, 60101, 62501, 65537, 69857, 76001, 76801, 160001, 162251, 163841, 307201, 453377, 524801, 544001, 670001, 952001, 976193, 980801
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OFFSET

1,1


COMMENTS

From Jon E. Schoenfield, Dec 02 2016, paraphrasing information from the Munafo link: (Start)
The decimal expansion of 10^10^10^10^2  1 would be 1 googolplex digits long, with each digit a 9. Many factors of this number can be identified using simple facts of modular arithmetic.
Since its digits are all 9's, it is divisible by 9=3*3. Since its digits are all 9's and the number of digits is even, it is divisible by 99 (as are 9999=99*101, 999999=99*10101, 99999999=99*1010101, etc.), and thus divisible by 11.
By the same principle, it is divisible by 9999, 99999, 99999999, and by any other number whose decimal expansion consists of k 9's where k is of the form 2^a * 5^b, where a and b are nonnegative integers up to 10^100 (see A003592) and all their divisors. Additional factors can be found using Fermat's Little Theorem.
Consequently, a large number of factors of 10^10^10^10^2  1 are known. (End)


LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..587
Dario Alejandro Alpern, Known prime factors of Googolplexplex  1
Dario Alejandro Alpern, Known 1digit prime factors of Googolplexplex  1
Robert P. Munafo, Notable Properties of Specific Numbers


EXAMPLE

10^10^10^10^2  1 = 10^10^10^100  1 = 999...999 (a total of a googolplex of nines).


CROSSREFS

Cf. A227246.
Sequence in context: A321678 A027416 A281905 * A163932 A007022 A011950
Adjacent sequences: A278832 A278833 A278834 * A278836 A278837 A278838


KEYWORD

nonn,fini


AUTHOR

Robert Munafo and Robert G. Wilson v, Nov 28 2016


STATUS

approved



