A280131 Partial sums of A029940 (Product_{d|n} phi(d)).

1, 2, 4, 6, 10, 14, 20, 28, 40, 56, 66, 98, 110, 146, 210, 274, 290, 434, 452, 708, 852, 952, 974, 1998, 2078, 2222, 2438, 3302, 3330, 7426, 7456, 8480, 8880, 9136, 9712, 23536, 23572, 23896, 24472, 40856, 40896, 61632, 61674, 65674, 74890, 75374, 75420

Offset

1,2

Comments

phi(n) is the number of totatives of n (A000010).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{i=1..n} A029940(i).

Maple

A029940:= [seq(mul(numtheory:-phi(d), d=numtheory:-divisors(n)), n=1..100)]:
ListTools:-PartialSums(A029940); # Robert Israel, Jan 11 2017

Mathematica

Accumulate@ Array[Product[EulerPhi@ d, {d, Divisors@ #}] &, 47] (* Michael De Vlieger, Dec 27 2016 *)

Prog

(Magma) [&+[&*[EulerPhi(d): d in Divisors(k)]: k in [1..n]]: n in [1..100]]

Crossrefs

Cf. A000010, A029940, A232533 (partial sums of A057661), A280132 (partial products of A029940).

Sequence in context: A241337 A103257 A103259 * A082380 A238871 A323595

Adjacent sequences: A280128 A280129 A280130 * A280132 A280133 A280134

Keyword

nonn

Author

Jaroslav Krizek, Dec 27 2016

Status

approved