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A201557
Proper GA1 numbers: terms of A197638 with at least three prime divisors counted with multiplicity.
5
183783600, 367567200, 1396755360, 1745944200, 2327925600, 3491888400, 6983776800, 80313433200, 160626866400, 252706217563800, 288807105787200, 336941623418400, 404329948102080, 505412435127600, 673883246836800, 1010824870255200, 2021649740510400, 112201560598327200
OFFSET
1,1
COMMENTS
Infinitely many terms are superabundant (SA) A004394; the smallest is 183783600.
Infinitely many terms are colossally abundant (CA) A004490; the smallest is 367567200.
Infinitely many terms are odd (and hence neither SA nor CA); the smallest is 1058462574572984015114271643676625.
See Section 5 of "On SA, CA, and GA numbers".
For additional terms, in factored form, see "Table of proper GA1 numbers up to 10^60", where SA and CA numbers are starred * and **.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..18408 (from the J.-L. Nicolas's table)
G. Caveney, J.-L. Nicolas, and J. Sondow, Robin's theorem, primes, and a new elementary reformulation of the Riemann Hypothesis, Integers 11 (2011), article A33.
G. Caveney, J.-L. Nicolas and J. Sondow, On SA, CA, and GA numbers, Ramanujan J., 29 (2012), 359-384 and arXiv:1112.6010.
J.-L. Nicolas, Computation of GA1 numbers, 2011.
FORMULA
A197638(n) if A001222(A197638(n)) > 2
EXAMPLE
183783600 = 2^4 * 3^3 * 5^2 * 7 * 11 * 13 * 17 is the smallest proper GA1 number.
MAPLE
See "Computation of GA1 numbers".
KEYWORD
nonn
AUTHOR
Geoffrey Caveney, Jean-Louis Nicolas, and Jonathan Sondow, Dec 03 2011
STATUS
approved