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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
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
KEYWORD
nonn
AUTHOR
Torlach Rush, Jan 13 2020
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)