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A341063
a(n) = Sum_{i+j<=m+1} t_i * t_j, where t_1 < ... < t_m are the totatives of n.
1
1, 1, 5, 7, 35, 11, 126, 70, 177, 90, 715, 142, 1365, 357, 680, 876, 3876, 645, 5985, 1300, 2856, 2255, 12650, 1916, 11675, 4446, 11061, 5362, 31465, 3260, 40920, 12376, 18920, 13192, 30240, 9066, 82251, 20691, 37752, 19080, 123410, 13062, 148995, 34870, 52080, 44781, 211876, 27640, 186102, 45650
OFFSET
1,3
COMMENTS
The totatives of n are the numbers k <= n with gcd(k,n) = 1.
If p is prime, a(p) = (p+2)*(p+1)*p*(p-1)/24.
It appears that 12*a(n) is always a multiple of n.
Conjecture: if p and q are distinct primes, a(p*q) = (p^2-p)*(q^2-q)*(p^2*q^2-p^2*q-p*q^2+p*q+2*p+2*q)/24.
LINKS
EXAMPLE
The totatives of 8 are 1, 3, 5, 7, so a(8) = 1*(1+3+5+7)+3*(1+3+5)+5*(1+3)+7*1 = 70.
MAPLE
f:= proc(n) local C, i, S, t;
C:= select(t -> igcd(t, n)=1, [$1..n]);
S:= ListTools:-PartialSums(C);
add(S[-i]*C[i], i=1..nops(C))
end proc:
map(f, [$1..100]);
CROSSREFS
Cf. A038566.
Sequence in context: A007911 A066172 A175667 * A018353 A176958 A196203
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Feb 04 2021
STATUS
approved