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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
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
Sequence in context: A266257 A115905 A292769 * A372686 A372517 A096134
KEYWORD
nonn,look
AUTHOR
J. M. Bergot and Robert Israel, May 09 2019
STATUS
approved

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