A308095 a(n) is the sum of sigma (i.e., A000203) over the totatives of n.
1, 1, 4, 5, 15, 7, 33, 19, 40, 26, 87, 27, 127, 50, 84, 82, 220, 59, 277, 90, 187, 140, 407, 103, 401, 193, 352, 207, 660, 127, 762, 309, 485, 339, 646, 244, 1098, 423, 677, 390, 1342, 268, 1480, 525, 758, 639, 1758, 416, 1666, 581, 1191, 770, 2250, 527, 1742, 821, 1527, 1016, 2786, 502, 3014
Offset: 1
Examples
a(3) = sigma(1) + sigma(2) = 4.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
- Robert Israel, Plot of a(n)/n^2 for 1 <= n <= 20000
Programs
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Maple
f:= proc(n) local k; add(numtheory:-sigma(k), k=select(t -> igcd(t,n)=1, [$1..n])) end proc; map(f, [$1..100]);
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PARI
a(n) = sum(k=1, n, if (gcd(n,k)==1, sigma(k))); \\ Michel Marcus, May 13 2019
Formula
a(n) = Sum_{1<=k<=n; gcd(k,n)=1} A000203(k).
Comments