A335334 Sum of the integers in the reduced residue system of A002110(n).

1, 6, 120, 5040, 554400, 86486400, 23524300800, 8045310873600, 4070927302041600, 3305592969257779200, 3074201461409734656000, 4094836346597766561792000, 6715531608420337161338880000, 12128250084807128913378017280000

Offset

1,2

Comments

Sum of the integers up to A002110(n) and coprime to A002110(n).

The sequence gives the sum of row n of A286941(n).

Links

Michael De Vlieger, Table of n, a(n) for n = 1..196

Eric Weisstein's World of Mathematics, Totative.

Formula

a(n) = A023896(A002110(n)).

a(n) = A002110(n)*A005867(n)/2 = A070826(n)*A005867(n).

a(n) = (A002110(n)*A038110(n+1)/2)*A058250(n).

Example

For n = 3: A002110(3) = 30, the reduced residue system of 30 is {1, 7, 11, 13, 17, 19, 23, 29}. The sum is a(3) = 120.

Mathematica

n = 15;
A002110 = Drop[FoldList[Times, 1, Prime[Range[n]]], 1];
A005867 = Drop[EulerPhi@FoldList[Times, 1, Prime@Range@n], 1];
A002110*A005867/2
(* Second program: *)
Map[# EulerPhi[#]/2 &, FoldList[Times, Prime@ Range@ 14]] (* Michael De Vlieger, Apr 07 2021 *)

Prog

(PARI) a(n) = my(P=factorback(primes(n))); P*eulerphi(P)/2; \\ Michel Marcus, Jun 02 2020

Crossrefs

Cf. A023896, A002110, A005867, A070826, A038110, A058250, A286941.

Sequence in context: A354333 A009445 A094273 * A094278 A093910 A002370

Adjacent sequences: A335331 A335332 A335333 * A335335 A335336 A335337

Keyword

nonn

Author

Jamie Morken, Jun 02 2020

Status

approved