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

1,2

Links

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

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A112186 A112187 A341621 * A324286 A265575 A352177

Adjacent sequences: A074090 A074091 A074092 * A074094 A074095 A074096

Keyword

nonn

Author

Amarnath Murthy, Aug 19 2002

Extensions

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

Status

approved