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A029939 a(n) = Sum_{d|n} phi(d)^2. 10
1, 2, 5, 6, 17, 10, 37, 22, 41, 34, 101, 30, 145, 74, 85, 86, 257, 82, 325, 102, 185, 202, 485, 110, 417, 290, 365, 222, 785, 170, 901, 342, 505, 514, 629, 246, 1297, 650, 725, 374, 1601, 370, 1765, 606, 697, 970, 2117, 430, 1801, 834, 1285, 870, 2705, 730, 1717, 814, 1625 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Equals the inverse Mobius transform (A051731) of A127473. [Gary W. Adamson, Aug 20 2008]

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

Multiplicative with a(p^e) = (p^(2*e)*(p-1)+2)/(p+1). - Vladeta Jovovic, Nov 19 2001

G.f.: Sum_{k>=1} phi(k)^2*x^k/(1 - x^k), where phi(k) is the Euler totient function (A000010). - Ilya Gutkovskiy, Jan 16 2017

a(n) = Sum_{k=1..n} phi(n/gcd(n, k)). - Ridouane Oudra, Nov 28 2019

MAPLE

with(numtheory): A029939 := proc(n) local i, j; j := 0; for i in divisors(n) do j := j+phi(i)^2; od; j; end;

# alternative

N:= 1000: # to get a(1)..a(N)

A:= Vector(N, 1):

for d from 2 to N do

  pd:= numtheory:-phi(d)^2;

  md:= [seq(i, i=d..N, d)];

  A[md]:= map(`+`, A[md], pd);

od:

seq(A[i], i=1..N); # Robert Israel, May 30 2016

MATHEMATICA

Table[Total[EulerPhi[Divisors[n]]^2], {n, 60}] (* Harvey P. Dale, Feb 04 2017 *)

PROG

(PARI) a(n) = sumdiv(n, d, eulerphi(d)^2); \\ Michel Marcus, Jan 17 2017

CROSSREFS

Cf. A051731, A062367, A127473.

Sequence in context: A042980 A048290 A306885 * A082198 A098871 A227623

Adjacent sequences:  A029936 A029937 A029938 * A029940 A029941 A029942

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 10 16:56 EDT 2020. Contains 336381 sequences. (Running on oeis4.)