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A329534 Irregular triangle read by rows: for n >= 1 row n lists the k from [1, 2, ... , n] such that A002378(k-1) = (k-1)*k == 0 (mod n). 1
1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 3, 4, 6, 1, 7, 1, 8, 1, 9, 1, 5, 6, 10, 1, 11, 1, 4, 9, 12, 1, 13, 1, 7, 8, 14, 1, 6, 10, 15, 1, 16, 1, 17, 1, 9, 10, 18, 1, 19, 1, 5, 16, 20, 1, 7, 15, 21, 1, 11, 12, 22, 1, 23, 1, 9, 16, 24, 1, 25 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

n-th row length gives 1 for n = 1, and 2^A001221(n) for n >= 2 , that is A034444(n). [Proof: Unique lifting theorem (e.g., Apostol, 5.30 (a), p.121) for this congruence, and only two solutions 1 and p for primes p. See also the Yuval Dekel, Sep 21 2003, comment in  A034444. - Wolfdieter Lang, Feb 05 2020]

REFERENCES

Tom M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1986.

LINKS

Table of n, a(n) for n=1..69.

EXAMPLE

The irregular triangle T(n,k) begins

n\k  1  2  3  4 ...

1:   1

2:   1  2

3:   1  3

4:   1  4

5:   1  5

6:   1  3  4  6

7:   1  7

8:   1  8

9:   1  9

10:  1  5  6 10

11:  1 11

12:  1  4  9 12

13:  1 13

14:  1  7  8 14

15:  1  6 10 15

16:  1 16

17:  1 17

18:  1  9 10 18

19:  1 19

20:  1  5 16 20

...

MATHEMATICA

Table[Select[Range@ n, Mod[-n + # (# - 1), n] == 0 &], {n, 25}] // Flatten (* Michael De Vlieger, Nov 18 2019 *)

PROG

(MAGMA) [[k: k in [1..n] | k^2 mod n eq k]: n in [1..38]];

(PARI) row(n) = select(x->(Mod(x, n) == Mod(x, n)^2), [1..n]); \\ Michel Marcus, Nov 19 2019

CROSSREFS

Cf. A000010, A000225, A000688, A000961, A001221, A006881, A006530, A007875, A020639, A024619, A034444, A077610, A135972, A309307.

Sequence in context: A222266 A077609 A077610 * A317746 A228179 A322313

Adjacent sequences:  A329531 A329532 A329533 * A329535 A329536 A329537

KEYWORD

nonn,easy,tabf

AUTHOR

Juri-Stepan Gerasimov, Nov 15 2019

EXTENSIONS

Edited by Wolfdieter Lang, Feb 05 2020

STATUS

approved

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Last modified July 23 17:41 EDT 2021. Contains 346259 sequences. (Running on oeis4.)