A074093 Number of values of k such that n = k - largest divisor of k (

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, 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, 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

Offset: 1

Author

Amarnath Murthy, Aug 19 2002

Keywords

• nonn

Examples

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

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

Programs

Mathematica

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 *)

PARI

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

Formula

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

Extensions

More terms from Benoit Cloitre and Vladeta Jovovic, Aug 21 2002