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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A072504

Adjacent sequences:  A070963 A070964 A070965 * A070967 A070968 A070969

KEYWORD

nonn

AUTHOR

Leroy Quet, May 16 2002

STATUS

approved

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Last modified June 23 18:45 EDT 2021. Contains 345402 sequences. (Running on oeis4.)