A335334 - OEIS

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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

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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