A201557 Proper GA1 numbers: terms of A197638 with at least three prime divisors counted with multiplicity.

183783600, 367567200, 1396755360, 1745944200, 2327925600, 3491888400, 6983776800, 80313433200, 160626866400, 252706217563800, 288807105787200, 336941623418400, 404329948102080, 505412435127600, 673883246836800, 1010824870255200, 2021649740510400, 112201560598327200

Offset: 1

Author

Geoffrey Caveney, Jean-Louis Nicolas, and Jonathan Sondow, Dec 03 2011

Keywords

• nonn

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 **.

Examples

			183783600 = 2^4 * 3^3 * 5^2 * 7 * 11 * 13 * 17 is the smallest proper GA1 number.
		

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.
• J.-L. Nicolas, Table of proper GA1 numbers up to 10^60, 2011.

Crossrefs

Cf. A000203, A001222, A067698, A197638, A197639, A201558, A216436.

Programs

Maple

See "Computation of GA1 numbers".

Formula

A197638(n) if A001222(A197638(n)) > 2