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A181538 T(n, k) = sum_(1 <= j <= k) [j | k] j mu(k / j) gcd(n, k), triangle read by rows. 3
1, 1, 2, 1, 1, 6, 1, 2, 2, 8, 1, 1, 2, 2, 20, 1, 2, 6, 4, 4, 12, 1, 1, 2, 2, 4, 2, 42, 1, 2, 2, 8, 4, 4, 6, 32, 1, 1, 6, 2, 4, 6, 6, 4, 54, 1, 2, 2, 4, 20, 4, 6, 8, 6, 40, 1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 110, 1, 2, 6, 8, 4, 12, 6, 16, 18, 8, 10, 48 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
T(n,k) = gcd(n,k) phi(k). Can be seen as a generalization of n -> phi(n^2) [A002618].
LINKS
Peter Luschny, Sequences related to Euler's totient function.
EXAMPLE
1
1,2
1,1,6
1,2,2,8
1,1,2,2,20
1,2,6,4,4,12
1,1,2,2,4,2,42
MAPLE
A181538 := (n, k) -> igcd(n, k)*phi(k);
MATHEMATICA
t[n_, k_] := Block[{j = Divisors@ k}, Plus @@ (#*MoebiusMu[k/#] & /@ j)] GCD[n, k]; Table[ t[n, k], {n, 12}, {k, n}] // Flatten (* Robert G. Wilson v, Jan 19 2011 *)
CROSSREFS
Cf. Row sums of triangle A181540.
Sequence in context: A333144 A306297 A053383 * A322128 A125731 A123361
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Oct 29 2010
STATUS
approved

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Last modified March 5 03:04 EST 2024. Contains 370537 sequences. (Running on oeis4.)