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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
OFFSET
1,4
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
Sequence in context: A046805 A034880 A257977 * A338669 A219254 A372833
KEYWORD
nonn
AUTHOR
Leroy Quet, May 16 2002
STATUS
approved