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A201557 Proper GA1 numbers: members 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 21 07:48 EDT 2020. Contains 337911 sequences. (Running on oeis4.)