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A224504 a(n) = number of elements of the row n in A214850. 1
2, 3, 6, 3, 3, 5, 3, 5, 4, 6, 4, 5, 4, 3, 8, 2, 3, 6, 3, 8, 6, 3, 8, 6, 2, 6, 8, 3, 4, 4, 4, 6, 4, 3, 8, 8, 2, 3, 7, 3, 8, 12, 3, 4, 8, 2, 8, 8, 3, 4, 8, 4, 8, 9, 4, 10, 6, 2, 5, 8, 2, 8, 6, 4, 6, 5, 3, 8, 4, 3, 8, 9, 4, 6, 7, 3, 8, 4, 4, 8, 5, 4, 8, 6, 5, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Number of multiplicative finite groups G(p) with elements {T(2n+1,k) /pZ} where T(2n+1,k) is the reduced trajectory of the Collatz problem whose elements are all odd and p <= A075684(n)+1.

LINKS

Michel Lagneau, Table of n, a(n) for n = 1..500

EXAMPLE

a(18) = 6 because there exists 6 finite groups given by the row 18 of A214850 where p = 2, 4, 6, 8, 12 and 18. The Collatz trajectory of the number 2*18+1 = 37 with odd numbers is T(37,k) = {37, 7, 11, 17, 13, 5, 1}, and the 6 groups G(p) are:

G(2) = {T(37,k)/2Z} = {1}

G(4) = {T(37,k)/4Z} = {1, 3}

G(6) = {T(37,k)/6Z} = {1, 5}

G(8) = {T(37,k)/8Z}  = {1, 3, 5, 7}

G(12) = {T(37,k)/12Z} = {1, 5, 7, 11}

G(18) = {T(37,k)/18Z} = {1, 5, 7, 11, 13, 17}

G(18) is a cyclic group because the element 5 (or 11) generates the group:

5^1 == 5, 5^2 == 7, 5^3 == 17, 5^4 == 13, 5^5 == 11, 5^6 == 1 (mod 18).

G(8) is not a cyclic group.

a(170) = 32 because there exists 32 finite groups with two elements given by the row 170 of A214850 where p = 2, 4, 6, 8, 10, 12, 18, 20, 24, 30, 34, 36, 38, 40, 60, 68, 72, 76, 90, 102, 114, 120, 136, 152, 170, 180, 190, 204, 228, 306, 340, 342. The Collatz trajectory of the number 2*170+1 = 341 with odd numbers is T(341,k) = {1, 341}.

CROSSREFS

Cf. A214850, A075680, A075684.

Sequence in context: A189971 A211605 A245886 * A216059 A261814 A240965

Adjacent sequences:  A224501 A224502 A224503 * A224505 A224506 A224507

KEYWORD

nonn

AUTHOR

Michel Lagneau, Apr 08 2013

STATUS

approved

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Last modified August 18 18:13 EDT 2017. Contains 290732 sequences.