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 A345891 a(n) = n + (n - 1) * phi(n). 1

%I #10 Jun 29 2021 08:09:28

%S 1,3,7,10,21,16,43,36,57,46,111,56,157,92,127,136,273,120,343,172,261,

%T 232,507,208,505,326,495,352,813,262,931,528,673,562,851,456,1333,704,

%U 951,664,1641,534,1807,904,1101,1036,2163,800,2065,1030,1651,1276,2757,1008,2215,1376

%N a(n) = n + (n - 1) * phi(n).

%C For 1 <= k <= n, add n if gcd(n,k) = 1, otherwise add 1. For n = 9 there are 6 numbers less than or equal to 9 that are relatively prime to 9 and 3 that are not. So a(9) = 9*6 + 3*1 = 57.

%F a(n) = Sum_{k=1..n} n^floor(1/gcd(n,k)).

%F a(n) = A062955(n) + n. - _Michel Marcus_, Jun 28 2021

%t Table[n + (n - 1)*EulerPhi[n], {n, 50}]

%o (PARI) a(n) = n + (n-1)*eulerphi(n); \\ _Michel Marcus_, Jun 28 2021

%Y Cf. A000010 (phi), A062955, A345892.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Jun 28 2021

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Last modified September 7 22:13 EDT 2024. Contains 375749 sequences. (Running on oeis4.)