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A055021 Smallest number k such that n iterations of sigma() are required for the result to be >= 2k. 5
6, 2, 9, 81 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

These are the first terms of A023196, A107912, A107913, A107914. - Jud McCranie, May 28 2005

a(5) > 4*10^9, if it exists. - Jud McCranie, May 28 2005

There are no more terms: sigma(2n) is never prime, so an even number needs at most two steps; sigma(n) is odd iff n is a square or twice a square. So A107914 (four recursive steps) contains only odd squares. Assume p prime so sigma(p^2) = p^2 + p + 1 = m^2 never meets the condition with p + 2k = m that (p + 2k)^2 = m^2. This implies the impossibility of a solution for numbers of the form p^(2i) and numbers of the form p^(2i)q^(2i). - Lambert Klasen (Lambert.Klasen(AT)gmx.net), Jun 06 2005

LINKS

Table of n, a(n) for n=1..4.

EXAMPLE

sigma(sigma(sigma(9))) = 24 >= 2*9, so a(3)=9.

CROSSREFS

Cf. A000203, A055020, A107912-A107914, A060800.

Sequence in context: A223536 A235362 A018801 * A260329 A141379 A100616

Adjacent sequences:  A055018 A055019 A055020 * A055022 A055023 A055024

KEYWORD

fini,full,nonn

AUTHOR

Jud McCranie, May 31 2000

STATUS

approved

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Last modified March 31 16:44 EDT 2020. Contains 333151 sequences. (Running on oeis4.)