A074093 - OEIS

%I #16 Feb 06 2019 17:19:10

%S 1,2,1,2,1,3,1,1,1,3,1,2,1,2,1,2,1,3,1,2,1,3,1,1,1,2,1,3,1,3,1,1,1,2,

%T 1,2,1,2,1,2,1,4,1,2,1,3,1,1,1,2,1,3,1,2,1,1,1,3,1,2,1,2,1,1,1,4,1,2,

%U 1,3,1,2,1,2,1,2,1,4,1,1,1,3,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,3,1,4,1,1,1

%N Number of values of k such that n = k - largest divisor of k (<k).

%H Antti Karttunen, <a href="/A074093/b074093.txt">Table of n, a(n) for n = 1..100000</a>

%F a(2n+1)=1; sum(k=1, n, a(k)) seems to be asymptotic to C*n with C=1.6... - _Benoit Cloitre_, Aug 21 2002

%e a(6) = 3 and the three values of k are 7,9 and 12.

%t f1[n_] := Count[Range[n, 2 n], _?(Differences[Take[Divisors[#], -2]] == {n} &)]; Join[{1}, Table[f1[n], {n, 2, 105}]] (* _Jayanta Basu_, Jul 30 2013 *)

%o (PARI) a(n)=sum(k=2,2*n,if(k- component(divisors(k),numdiv(k)-1)-n,0,1))

%Y Cf. A073932, A073933, A073934, A073935, A060681.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Aug 19 2002

%E More terms from _Benoit Cloitre_ and _Vladeta Jovovic_, Aug 21 2002