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A181552 T(n,k) = gcd(n,k) A181549(k), triangle read by rows. 2
1, 1, 6, 1, 3, 12, 1, 6, 4, 20, 1, 3, 4, 5, 30, 1, 6, 12, 10, 6, 72, 1, 3, 4, 5, 6, 12, 56, 1, 6, 4, 20, 6, 24, 8, 80, 1, 3, 12, 5, 6, 36, 8, 10, 99, 1, 6, 4, 10, 30, 24, 8, 20, 11, 180, 1, 3, 4, 5, 6, 12, 8, 10, 11, 18, 132, 1, 6, 12, 20, 6, 72, 8, 40, 33, 36, 12, 240 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A181549(n) = sum{k|n} k mu_2(n/k) is a variant of Euler's phi function relative to the Moebius function of order 2.

LINKS

Table of n, a(n) for n=1..78.

Peter Luschny, Sequences related to Euler's totient function.

EXAMPLE

1,

1,6,

1,3,12,

1,6,.4,20,

1,3,.4,.5,30,

1,6,12,10,.6,72,

1,3,.4,.5,.6,12,56,

1,6,.4,20,.6,24,.8,80,

MAPLE

A181552 := (n, k) -> igcd(n, k)*A181549(k);

MATHEMATICA

mu2[1] = 1; mu2[n_] := Sum[Boole[Divisible[n, d^2]]*MoebiusMu[n/d^2]*MoebiusMu[n/d], {d, Divisors[n]}]; A181549[n_] := Sum[k*mu2[n/k], {k, Divisors[n]}]; t[n_, k_] := GCD[n, k]*A181549[k]; Table[t[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-Fran├žois Alcover, Feb 05 2014 *)

CROSSREFS

Cf. A130212, A181538, row sums of triangle is A181553.

Sequence in context: A259731 A176399 A273081 * A294347 A229606 A101023

Adjacent sequences:  A181549 A181550 A181551 * A181553 A181554 A181555

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Oct 30 2010

STATUS

approved

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Last modified September 25 09:32 EDT 2021. Contains 347654 sequences. (Running on oeis4.)