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A062380 a(n) = Sum_{i|n,j|n} phi(i)*phi(j)/phi(gcd(i,j)), where phi is Euler totient function. 8
1, 4, 7, 14, 13, 28, 19, 42, 37, 52, 31, 98, 37, 76, 91, 114, 49, 148, 55, 182, 133, 124, 67, 294, 113, 148, 163, 266, 85, 364, 91, 290, 217, 196, 247, 518, 109, 220, 259, 546, 121, 532, 127, 434, 481, 268, 139, 798, 229, 452, 343, 518, 157, 652, 403, 798, 385 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Multiplicative with a(p^e) = 1 + sum_{k=1..e} (2k+1)(p^k-p^{k-1}) = ((2e+1)p^(e+1) - (2e+3)p^e+2)/(p-1). - Mitch Harris, May 24 2005

A176003 is a subsequence. - Peter Luschny, Sep 12 2012

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = Sum_{d|n} phi(d)*tau(d^2).

a(n) = Sum_{c|n,d|n} phi(lcm(c,d)). - Peter Luschny, Sep 10 2012

EXAMPLE

Let p be a prime then a(p) = phi(1)*tau(1)+phi(p)*tau(p^2) = 1+(p-1)*3 = 3*p-2. - Peter Luschny, Sep 12 2012

MAPLE

with(numtheory):

a:= n->  add(phi(d)*tau(d^2), d=divisors(n)):

seq(a(n), n=1..60);  # Alois P. Heinz, Sep 12 2012

MATHEMATICA

a[n_] := DivisorSum[n, EulerPhi[#] DivisorSigma[0, #^2]&]; Array[a, 60] (* Jean-Fran├žois Alcover, Dec 05 2015 *)

PROG

(Sage)

def A062380(n) :

    d = divisors(n); cp = cartesian_product([d, d])

    return reduce(lambda x, y: x+y, map(euler_phi, map(lcm, cp)))

[A062380(n) for n in (1..57)]  # Peter Luschny, Sep 10 2012

(PARI) a(n)=sumdiv(n, i, eulerphi(i)*sumdiv(n, j, eulerphi(j)/eulerphi(gcd(i, j)))) \\ Charles R Greathouse IV, Sep 12 2012

CROSSREFS

Cf. A000005, A000010, A060648.

Sequence in context: A243707 A055675 A310825 * A310826 A310827 A310828

Adjacent sequences:  A062377 A062378 A062379 * A062381 A062382 A062383

KEYWORD

nonn,mult

AUTHOR

Vladeta Jovovic, Jul 07 2001

STATUS

approved

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Last modified April 14 22:47 EDT 2021. Contains 342971 sequences. (Running on oeis4.)