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A317746 Irregular triangle read by rows in which row n lists the divisors k of n such that k^n + n^k == 0 mod (k + n). 0
1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 3, 6, 1, 7, 1, 2, 8, 1, 3, 9, 1, 10, 1, 11, 1, 4, 6, 12, 1, 13, 1, 7, 14, 1, 3, 5, 15, 1, 16, 1, 17, 1, 6, 9, 18, 1, 19, 1, 5, 20, 1, 3, 7, 21, 1, 22, 1, 23, 1, 3, 8, 12, 24, 1, 5, 25, 1, 13, 26, 1, 3, 9, 27, 1, 4, 28, 1, 29, 1, 6, 10, 15, 30 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Triangle read by rows in which row n lists the type-1 divisors of n. For each divisor k of n, call k a type-r divisor of n if (r*k)^n + n^(r*k) == 0 mod (r*k + n), r >= 1.

Triangle read by rows in which row n lists the smallest types r of divisor k of n such that (r*k)^n + n^(r*k) == 0 mod (r*k + n) begins:

  1;

  1,  1;

  1,  1;

  1,  2,  1;

  1,  1;

  1,  3,  1,  1;

  1,  1;

  1,  1,  2,  1;

  1,  1,  1;

  1,  3,  2,  1;

  1,  1;

  1,  2,  3,  1,  1,  1;

..., where the total number of type-1 divisors of n is the sum of the number of all trivial divisors of n and a certain number of nontrivial divisors of n, namely: 1+0, 2+0, 2+0, 2+0, 2+0, 2+1, 2+0, 2+1, 2+1, 2+0, 2+0, 2+2, ...

LINKS

Table of n, a(n) for n=1..83.

EXAMPLE

Triangle begins:

  1;

  1,  2;

  1,  3;

  1,  4;

  1,  5;

  1,  3,  6;

  1,  7;

  1,  2,  8;

  1,  3,  9;

  1, 10;

  1, 11;

  1,  4,  6, 12;

MATHEMATICA

a[n_] := Select[ Divisors@ n, Mod[PowerMod[#, n, # + n] + PowerMod[n, #, # + n], # + n] == 0 &]; Array[a, 30] // Flatten (* Robert G. Wilson v, Aug 06 2018 *)

PROG

(MAGMA) [[k: k in [ 1..n] | Denominator(n/k) eq 1 and Denominator((k^n+n^k)/(k+n)) eq 1]: n in [1..30]]

CROSSREFS

Cf. A027750, A070824.

Sequence in context: A077609 A077610 A329534 * A228179 A322313 A322315

Adjacent sequences:  A317743 A317744 A317745 * A317747 A317748 A317749

KEYWORD

nonn,tabf

AUTHOR

Juri-Stepan Gerasimov, Aug 06 2018

STATUS

approved

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Last modified August 9 12:53 EDT 2022. Contains 356026 sequences. (Running on oeis4.)