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A279401 Irregular triangle read by rows. Row n gives the orders of the primes of row n of the irregular triangle A279399 modulo A033949(n). 1
2, 2, 2, 2, 2, 2, 4, 4, 2, 4, 4, 4, 2, 4, 4, 4, 4, 2, 4, 4, 2, 6, 6, 6, 2, 6, 6, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 6, 6, 6, 4, 2, 4, 4, 2, 4, 2, 8, 8, 4, 8, 8, 2, 8, 4, 8, 2, 10, 10, 10, 10, 10, 10, 2, 10, 5, 12, 12, 3, 4, 12, 6, 12, 2, 6, 6, 6, 6, 3, 2, 2, 6, 6, 6, 12, 4, 12, 12, 6, 12, 6, 6, 4, 12, 4, 4, 2, 4, 4, 2, 4, 2, 2, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The length of row n is given by A279400(n).

See the A279399 comments.

The entries in row n are proper divisors of phi(A033949(n)), where phi(n) = A000010(n).

  This is because no A033949 number has a primitive root.

LINKS

Table of n, a(n) for n=1..105.

FORMULA

T(n, k) = order(A279399(n, k)) (mod A033949(n)), n >= 1, k = 1..A279400(n).

EXAMPLE

The irregular triangle T(n, k) begins (here N = A033949(n)):

n,   N \ k 1  2  3  4  5  6  7  8  9 10 ...

1,   8:    2  2  2

2,  12:    2  2  2

3,  15:    4  4  2  4

4,  16:    4  4  2  4  4

5,  20:    4  4  2  4  4  2

6,  21:    6  6  6  2  6  6

7,  24:    2  2  2  2  2  2  2

8,  28:    6  6  6  2  6  6  6

9,  30:    4  2  4  4  2  4  2

10, 32:    8  8  4  8  8  2  8  4  8  2

11, 33:   10 10 10 10 10 10  2 10  5

12, 35:   12 12  3  4 12  6 12  2  6

13, 36:    6  6  6  3  2  2  6  6  6

14, 39:   12  4 12 12  6 12  6  6  4 12

15, 40:    4  4  2  4  4  2  4  2  2  4

...

The sequence of phi(N) begins: 4, 4, 8, 8, 8, 12, 8, 12, 8, 16, 20, 24, 12, 24, 16, ...

n = 2, N = 12:  5^2 == 7^2 == 11^2 == 1 (mod 12), therefore 2 is the least positive power k for each of the three primes p of row 2 of A279399 which satisfies p^k == 1 (mod A033949(2)).

CROSSREFS

Cf. A000010, A033949, A279399, A279400.

Sequence in context: A072924 A247869 A036263 * A168514 A060447 A268045

Adjacent sequences:  A279398 A279399 A279400 * A279402 A279403 A279404

KEYWORD

nonn,tabf

AUTHOR

Wolfdieter Lang, Jan 30 2017

STATUS

approved

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Last modified March 18 12:10 EDT 2019. Contains 321283 sequences. (Running on oeis4.)