A280164 - OEIS

%I #15 Dec 28 2016 02:26:45

%S 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,

%T 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,

%U 1,2,0,5,0,0,3,2,2,2,0,5,0,0,0,6,1,1,1

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

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

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

%H Peter Kagey, <a href="/A280164/b280164.txt">Table of n, a(n) for n = 1..2000</a>

%e For a(21) = 2 the anagrams are:

%e   (1) 21 and 2*21 in base 8 (i.e. 25_8 and 52_8);

%e   (2) 21 and 5*21 in base 13.

%e For a(40) = 5 the anagrams are:

%e   (1) 40 and  2*40 in base 5 (i.e. 130_5 and 310_5);

%e   (2) 40 and  2*40 in base 11;

%e   (3) 40 and 10*40 in base 21;

%e   (4) 40 and  8*40 in base 29;

%e   (5) 40 and  7*40 in base 31.

%Y Cf. A279689, A279963.

%K nonn,base

%O 1,21

%A _Peter Kagey_, Dec 27 2016