A069928 Number of k, 1<=k<=n, such that tau(k) divides sigma(k) where tau(x) is the number of divisors of x and sigma(x) the sum of divisors of x.

1, 1, 2, 2, 3, 4, 5, 5, 5, 5, 6, 6, 7, 8, 9, 9, 10, 10, 11, 12, 13, 14, 15, 15, 15, 15, 16, 16, 17, 18, 19, 19, 20, 20, 21, 21, 22, 23, 24, 24, 25, 26, 27, 28, 29, 30, 31, 31, 32, 32, 33, 33, 34, 35, 36, 37, 38, 38, 39, 40, 41, 42, 42, 42, 43, 44, 45, 46, 47, 48, 49, 49, 50, 50

Offset

1,3

Comments

Number of arithmetic numbers <= n, cf. A003601; partial sums of A245656. - Reinhard Zumkeller, Jul 28 2014

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Wikipedia, Arithmetic number

Formula

a(n)=Card(k: 1<=k<=n : sigma(k) == 0 (mod tau(k) ) : lim n -> infinity a(n)/n=C=0, 8...

Mathematica

Accumulate[Table[If[Divisible[DivisorSigma[1, n], DivisorSigma[0, n]], 1, 0], {n, 80}]] (* Harvey P. Dale, Oct 06 2020 *)

Prog

(PARI) for(n=1, 150, print1(sum(i=1, n, if(sigma(i)%numdiv(i), 0, 1)), ", "))
(Haskell)
a069928 n = a069928_list !! (n-1)
a069928_list = scanl1 (+) a245656_list
-- Reinhard Zumkeller, Jul 28 2014

Crossrefs

Cf. A000005, A000203, A003601, A245656.

Sequence in context: A342880 A337774 A371263 * A135585 A081094 A361674

Adjacent sequences: A069925 A069926 A069927 * A069929 A069930 A069931

Keyword

easy,nonn

Author

Benoit Cloitre, May 05 2002

Status

approved