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

1,2

Links

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

Formula

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

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]

Crossrefs

Main diagonal of A059379, A059380.

Sequence in context: A037797 A071846 A357036 * A052141 A062793 A300398

Adjacent sequences: A067855 A067856 A067857 * A067859 A067860 A067861

Keyword

nonn

Author

Leroy Quet, Feb 15 2002

Status

approved