A070966 a(n) = Sum_{k|n, k<=sqrt(n)} phi(k); where the sum is over the positive divisors, k, of n, which are <= the square root of n; and phi(k) is the Euler totient function.

1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 4, 1, 2, 3, 4, 1, 4, 1, 4, 3, 2, 1, 6, 5, 2, 3, 4, 1, 8, 1, 4, 3, 2, 5, 8, 1, 2, 3, 8, 1, 6, 1, 4, 7, 2, 1, 8, 7, 6, 3, 4, 1, 6, 5, 10, 3, 2, 1, 12, 1, 2, 9, 8, 5, 6, 1, 4, 3, 12, 1, 12, 1, 2, 7, 4, 7, 6, 1, 12, 9, 2, 1, 14, 5, 2, 3, 8, 1, 16, 7, 4, 3, 2, 5, 12, 1, 8, 9, 12

Offset

1,4

Links

Table of n, a(n) for n=1..100.

Formula

G.f.: Sum_{n>=1} A000010(n)*x^(n^2)/(1-x^n). - Mircea Merca, Feb 23 2014

Example

a(30) = phi(1) + phi(2) + phi(3) + phi(5) = 1 + 1 + 2 + 4 = 8 because 1, 2, 3 and 5 are the positive divisors of 30 which are <= sqrt(30).

Maple

A070966 := proc(n)
    local a, k ;
    a := 0 ;
    for k in numtheory[divisors](n) do
        if k^2 <= n then
            a := a+numtheory[phi](k) ;
        end if;
    end do:
    a ;
end proc: # R. J. Mathar, May 27 2016

Prog

(PARI) a(n) = sumdiv(n, d, eulerphi(d)*(d^2 <= n)); \\ Michel Marcus, Dec 19 2017

Crossrefs

Cf. A000010, A066839.

Sequence in context: A046805 A034880 A257977 * A338669 A219254 A372833

Adjacent sequences: A070963 A070964 A070965 * A070967 A070968 A070969

Keyword

nonn

Author

Leroy Quet, May 16 2002

Status

approved