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A331314 Dirichlet convolution of the identity function with the reduced totient function. 0
1, 3, 5, 8, 9, 15, 13, 18, 21, 27, 21, 38, 25, 39, 41, 40, 33, 63, 37, 68, 59, 63, 45, 84, 65, 75, 81, 98, 57, 123, 61, 88, 95, 99, 105, 156, 73, 111, 113, 150, 81, 177, 85, 158, 165, 135, 93, 184, 133, 195 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence differs from A018804 when A002322 differs from A000010.

LINKS

Table of n, a(n) for n=1..50.

FORMULA

a(n) = Sum_{d|n} d*A002322(n/d).

MATHEMATICA

a[n_] := DivisorSum[n, # * CarmichaelLambda[n/#] &]; Array[a, 50] (* Amiram Eldar, Jan 13 2020 *)

PROG

(PARI) a(n) = sumdiv(n, d, d * lcm(znstar(n/d)[2])); \\ Daniel Suteu, Jan 13 2020

(MAGMA) [1] cat [&+[d*CarmichaelLambda(n div d):d in Set(Divisors(n)) diff {n}]+n:n in [2..60]]; // Marius A. Burtea, Jan 14 2020

CROSSREFS

Cf. A000010 (phi), A002322 (psi), A018804 (Pillai's arithmetical function).

Sequence in context: A138808 A185456 A308405 * A018804 A032682 A022769

Adjacent sequences:  A331311 A331312 A331313 * A331315 A331316 A331317

KEYWORD

nonn

AUTHOR

Torlach Rush, Jan 13 2020

STATUS

approved

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Last modified April 3 14:25 EDT 2020. Contains 333197 sequences. (Running on oeis4.)