|
| |
|
|
A109325
|
|
Zsigmondy numbers for a = 3, b = 2: Zs(n, 3, 2) is the greatest divisor of 3^n - 2^n (A001047) that is relatively prime to 3^m - 2^m for all positive integers m < n.
|
|
5
| |
|
|
1, 5, 19, 13, 211, 7, 2059, 97, 1009, 11, 175099, 61, 1586131, 463, 3571, 6817, 129009091, 577, 1161737179, 4621, 267331, 35839, 94134790219, 5521, 4015426801, 320503, 397760329, 369181, 68629840493971, 7471, 617671248800299, 43112257
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| The full factorization is multiplicative; meaning that the composition of factors is determined by the prime-factorization of n.
|
|
|
LINKS
| Eric Weisstein's World of Mathematics, Zsigmondy's Theorem
|
|
|
EXAMPLE
| Let n be 7; then the factorization of g(n) := 3^n-2^n is then g(7) = A(7) = 2059 since n is prime; let n be 3 then the factorization of g(3) = A(3) = 19 since n is prime; let n be 21, then the factorization is g(21) = A(3)*A(7)*A(21); and whether n is composite or not, with each n (at least) one new factor occurs besides the factors determined by the prime factors of n - so it is not purely multiplicative.
|
|
|
CROSSREFS
| Cf. A064078-A064083, A109347, A109348, A109349.
Sequence in context: A089082 A106229 A129734 * A169698 A166639 A032731
Adjacent sequences: A109322 A109323 A109324 * A109326 A109327 A109328
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Gottfried Helms (helms(AT)uni-kassel.de), Aug 09 2005
|
|
|
EXTENSIONS
| Edited and extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Aug 26 2005
|
| |
|
|
