

A057789


a(n) = Sum_{k = 1..n, gcd(k,n)=1} k*(nk).


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
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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(n1).
If n/2 is an odd prime, a(n) = A000292(n2)/2.
If n/3 is a prime other than 3, a(n) = A000292(n3)*2*n/(3*(n2)). (End)


EXAMPLE

Since 1, 3, 5 and 7 are relatively prime to 8 and are <= 8, a(8) = 1*(81) +3*(83) +5*(85) +7*(87) = 44.


MAPLE

f:= proc(n) local i;
2*add(`if`(igcd(i, n)=1, i*(ni), 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*(nk))); \\ 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



