A280164 Number of integer pairs (k, b) such that n and k*n are anagrams in base-b (k > 1).

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 2, 0, 0, 3, 0, 0, 1, 1, 0, 2, 0, 2, 1, 0, 1, 1, 0, 0, 2, 5, 0, 1, 0, 1, 2, 0, 0, 6, 0, 0, 1, 1, 0, 0, 2, 4, 2, 0, 0, 3, 0, 0, 1, 1, 2, 3, 0, 1, 1, 2, 0, 5, 0, 0, 3, 2, 2, 2, 0, 5, 0, 0, 0, 6, 1, 1, 1

Offset

1,21

Comments

(b-1) divides n*(k-1) for all (k, b).

1, 2, ... first appear at 8, 21, 24, 56, 40, 48, 96, 144, 432, 120, 264, 168, 360, 312, 336, 560, 240 respectively.

Links

Peter Kagey, Table of n, a(n) for n = 1..2000

Example

For a(21) = 2 the anagrams are:
  (1) 21 and 2*21 in base 8 (i.e. 25_8 and 52_8);
  (2) 21 and 5*21 in base 13.
For a(40) = 5 the anagrams are:
  (1) 40 and  2*40 in base 5 (i.e. 130_5 and 310_5);
  (2) 40 and  2*40 in base 11;
  (3) 40 and 10*40 in base 21;
  (4) 40 and  8*40 in base 29;
  (5) 40 and  7*40 in base 31.

Crossrefs

Cf. A279689, A279963.

Sequence in context: A259481 A132825 A259480 * A049597 A210951 A348127

Adjacent sequences: A280161 A280162 A280163 * A280165 A280166 A280167

Keyword

nonn,base

Author

Peter Kagey, Dec 27 2016

Status

approved