The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A307997 a(n) is the sum of A023896(k) over the totatives of n. 2
 1, 1, 2, 4, 9, 11, 25, 35, 53, 52, 109, 87, 188, 174, 218, 255, 432, 301, 622, 492, 636, 633, 1109, 725, 1288, 1113, 1468, 1287, 2275, 1121, 2801, 2305, 2598, 2499, 3227, 2266, 4760, 3550, 4229, 3449, 6556, 3311, 7628, 5527, 5846, 6199, 10017, 5736, 10453, 7282, 9654, 8832, 14451, 8143, 13060 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) <= A213544(n-1) for n >= 2, with equality if and only if n is prime. - Robert Israel, May 10 2019 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 Robert Israel, Plot of a(n)/n^3 for n=3 to 20000 FORMULA a(n) = Sum_{1<=k<=n; gcd(k,n)=1} A023896(k). a(n) = Sum_{k=1..n} k*A143620(n,k). EXAMPLE a(6) = 11 because the totatives of 6, i.e. the numbers from 1 to 6 that are coprime to 6, are 1 and 5, A023896(1) = 1 and A023896(5) = 1+2+3+4=10, and 1+10=11. MAPLE A023896:= proc(n) option remember; convert(select(t -> igcd(t, n)=1, [\$1..n]), `+`) end proc: f:= n -> convert(map(A023896, select(t -> igcd(t, n)=1, [\$1..n])), `+`): map(f, [\$1..100]); MATHEMATICA A023896[n_] := If[n == 1, 1, (n/2) EulerPhi[n]]; a[n_] := Sum[Boole[GCD[n, k] == 1] A023896[k], {k, 1, n}]; Array[a, 100] (* Jean-François Alcover, Jul 31 2020 *) PROG (PARI) s(n) = if(n<2, n>0, n*eulerphi(n)/2); \\ A023896 a(n) = sum(k=1, n, if (gcd(n, k)==1, s(k))); \\ Michel Marcus, May 10 2019 CROSSREFS Cf. A023896, A143620, A213544. Sequence in context: A266257 A115905 A292769 * A372686 A372517 A096134 Adjacent sequences: A307994 A307995 A307996 * A307998 A307999 A308000 KEYWORD nonn,look AUTHOR J. M. Bergot and Robert Israel, May 09 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 28 15:56 EDT 2024. Contains 372916 sequences. (Running on oeis4.)