A280132 -id:A280132 - cp's OEIS frontend

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

Jaroslav Krizek, Dec 27 2016

nonn

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

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

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

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

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

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

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

A280133 Partial products of A057661 (Sum_{d|n} psi(d)).

Original entry on oeis.org

1, 2, 8, 48, 528, 5808, 127776, 2811072, 87143232, 2788583424, 156160671744, 6090266198016, 481131029643264, 31273516926812160, 2314240252584099840, 199024661722232586240, 27266378655945864314880, 2508506836347019516968960, 431463175851687356918661120

Offset: 1

Jaroslav Krizek, Dec 27 2016

nonn

psi(n) is the sum of the totatives of n (A023896).

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

[&*[&+[&+[h: h in [1..d] | GCD(h,d) eq 1]: d in Divisors(k)]: k in [1..n]]: n in [1..1000]]

FoldList[Times[#1, #2] &, Array[Sum[Total@ Select[Range@ d, CoprimeQ[#, d] &], {d, Divisors@ #}] &, 19]] (* Michael De Vlieger, Dec 27 2016 *)

a(n) = Product_{i=1..n} A057661(i).

cp's OEIS Frontend

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

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