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A069931
Number of k, 1<=k<=n, such that k divides sigma(n).
1
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)).
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 * A373534 A209152 A209158
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, May 05 2002
EXTENSIONS
Corrected by Vaclav Kotesovec, Feb 16 2019
STATUS
approved