|
%I #17 Jun 13 2022 07:52:55
%S 1,1,2,2,4,2,6,4,5,3,8,3,10,4,6,4,12,4,13,4,11,6,14,3,10,6,12,6,17,3,
%T 16,7,10,9,13,4,18,7,11,4,22,3,26,8,9,7,23,5,18,7,13,6,25,4,24,8,21,6,
%U 18,3,18,10,12,14,16,4,26,8,17,7,31,5,30,6,11,13,26,7,25,6,16,10,35,4,18,11
%N Number of divisors of n^4 - 1 that are not greater than n.
%C a(n) = #{d: d<=n and A123865(n) mod d = 0};
%C a(n)>1 for n>2, see A129293 for m such that a(m)=2: a(A129293(n))=2.
%H Reinhard Zumkeller, <a href="/A129292/b129292.txt">Table of n, a(n) for n = 1..1000</a>
%e a(100) = #{1,3,9,11,33,73,99} = 7.
%p f:= n -> nops(select(`<=`,numtheory:-divisors(n^4-1),n)):
%p 1,seq(f(n), n=2..100); # _Robert Israel_, Sep 21 2014
%t Table[Count[Divisors[n^4-1],_?(#<=n&)],{n,90}] (* _Harvey P. Dale_, Aug 13 2014 *)
%o (PARI) a(n) = if (n==1, 1, sumdiv(n^4-1, d, d <= n)); \\ _Michel Marcus_, Sep 21 2014
%Y Cf. A129294, A129296.
%K nonn
%O 1,3
%A _Reinhard Zumkeller_, Apr 09 2007
|
