A067858 J_n(n), where J is the Jordan function, J_n(n) = n^n product{p|n}(1 - 1/p^n), the product is over the distinct primes, p, dividing n.

1, 3, 26, 240, 3124, 45864, 823542, 16711680, 387400806, 9990233352, 285311670610, 8913906892800, 302875106592252, 11111328602468784, 437893859848932344, 18446462598732840960, 827240261886336764176, 39346257879101671328376, 1978419655660313589123978

Offset: 1

Author

Leroy Quet, Feb 15 2002

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..350

Crossrefs

Main diagonal of A059379, A059380.

Programs

Maple

with(numtheory):
a:= n-> n^n*mul(1-1/p^n, p=factorset(n)):
seq(a(n), n=1..20);  # Alois P. Heinz, Jan 09 2015

Mathematica

JordanTotient[n_,k_:1]:=DivisorSum[n, #^k*MoebiusMu[n/#]&]/; (n>0)&&IntegerQ[n]; A067858[n_]:=JordanTotient[n,n]; Array[A067858,20]

Formula

J_n(n) = sum{k|n} mu(n/k) k^n, where mu() is the Moebius function.