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

1,3

Comments

a(n) <= A024916(n-1) for n >= 2, with equality if and only if n is prime.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Robert Israel, Plot of a(n)/n^2 for 1 <= n <= 20000

Formula

a(n) = Sum_{1<=k<=n; gcd(k,n)=1} A000203(k).

Example

a(3) = sigma(1) + sigma(2) = 4.

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]);

Prog

(PARI) a(n) = sum(k=1, n, if (gcd(n, k)==1, sigma(k))); \\ Michel Marcus, May 13 2019

Crossrefs

Cf. A000203, A024916, A307997.

Sequence in context: A222501 A225204 A363817 * A321348 A257311 A369790

Adjacent sequences: A308092 A308093 A308094 * A308096 A308097 A308098

Keyword

nonn,look

Author

J. M. Bergot and Robert Israel, May 12 2019

Status

approved