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 A057789 a(n) = Sum_{k = 1..n, gcd(k,n)=1} k*(n-k). 1
 0, 1, 4, 6, 20, 10, 56, 44, 84, 60, 220, 92, 364, 182, 280, 344, 816, 318, 1140, 520, 840, 770, 2024, 760, 2100, 1300, 2196, 1540, 4060, 1240, 4960, 2736, 3520, 2992, 4760, 2580, 8436, 4218, 5928, 4240, 11480, 3612, 13244, 6380, 8040, 7590, 17296, 6128 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Equal to convolution sum over positive integers, k, where k<=n and gcd(k,n)=1, except in first term, where the convolution sum is 1 instead of 0. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA From Robert Israel, Sep 29 2019: (Start) If n is prime, a(n) = A000292(n-1). If n/2 is an odd prime, a(n) =  A000292(n-2)/2. If n/3 is a prime other than 3, a(n) = A000292(n-3)*2*n/(3*(n-2)). (End) EXAMPLE Since 1, 3, 5 and 7 are relatively prime to 8 and are <= 8, a(8) = 1*(8-1) +3*(8-3) +5*(8-5) +7*(8-7) = 44. MAPLE f:= proc(n) local i;   2*add(`if`(igcd(i, n)=1, i*(n-i), 0), i=1..n/2) end proc: f(2):= 1: map(f, [\$1..100]); # Robert Israel, Sep 29 2019 PROG (PARI) a(n) = sum(k=1, n, if (gcd(n, k)==1, k*(n-k))); \\ Michel Marcus, Sep 29 2019 CROSSREFS Cf. A000292. Sequence in context: A053892 A013126 A012969 * A174936 A123169 A205955 Adjacent sequences:  A057786 A057787 A057788 * A057790 A057791 A057792 KEYWORD nonn,look AUTHOR Leroy Quet, Nov 04 2000 STATUS approved

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Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)