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

1,1

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.

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

Crossrefs

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

Sequence in context: A179586 A234384 A226589 * A234050 A253941 A230222

Adjacent sequences: A201554 A201555 A201556 * A201558 A201559 A201560

Keyword

nonn

Author

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

Status

approved