A069931 Number of k, 1<=k<=n, such that k divides sigma(n).

1, 1, 2, 1, 3, 5, 3, 3, 1, 5, 5, 4, 3, 7, 7, 1, 5, 3, 5, 6, 5, 8, 7, 10, 1, 7, 7, 7, 7, 10, 5, 5, 9, 7, 9, 3, 3, 11, 7, 10, 7, 10, 5, 11, 7, 11, 9, 4, 3, 3, 11, 5, 7, 14, 11, 14, 9, 11, 11, 14, 3, 11, 7, 1, 11, 13, 5, 11, 11, 13, 11, 7, 3, 7, 5, 11, 11, 14, 9, 6, 2, 11, 11, 10, 11, 11, 15, 16

Offset

1,3

Comments

Sequence does not give the number of all integers dividing sigma(n) which is tau(sigma(n)) (for some n and some m>n m divides sigma(n)).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Vaclav Kotesovec, Plot of Sum_{k=1..n} a(k)/(n*log(n)^2) for n = 2..20000

Formula

Asymptotically (still conjectured): sum(k=1, n, a(k)) = C*n*log(n)^2 + o(n*log(n)^2) with C=0.35...

Maple

A069931 := proc(n)
    local a, k ;
    a := 0 ;
    for k from 1 to n do
        if modp(numtheory[sigma](n), k) = 0 then
            a := a+1 ;
        end if;
    end do:
    a;
end proc:
seq(A069931(n), n=1..80) ; # R. J. Mathar, Jan 15 2021

Mathematica

Table[Length[Select[Range[n], Divisible[DivisorSigma[1, n], #]&]], {n, 1, 100}] (* Vaclav Kotesovec, Feb 16 2019 *)

Prog

(PARI) for(n=1, 150, print1(sum(i=1, n, if(sigma(n)%i, 0, 1)), ", "))

Crossrefs

Cf. A062068.

Sequence in context: A368070 A322942 A060083 * A209152 A209158 A209135

Adjacent sequences: A069928 A069929 A069930 * A069932 A069933 A069934

Keyword

easy,nonn

Author

Benoit Cloitre, May 05 2002

Extensions

Corrected by Vaclav Kotesovec, Feb 16 2019

Status

approved