A092843 - OEIS

A092843

a(n) = Sum_{k|n, k>1} phi(k-1), where phi() is the Euler phi function.

0, 1, 1, 3, 2, 6, 2, 9, 5, 9, 4, 18, 4, 15, 9, 17, 8, 26, 6, 29, 11, 17, 10, 46, 10, 25, 17, 35, 12, 48, 8, 47, 21, 29, 20, 62, 12, 43, 23, 59, 16, 68, 12, 61, 33, 35, 22, 100, 18, 59, 29, 59, 24, 90, 24, 81, 31, 49, 28, 136, 16, 69, 45, 83, 38, 86, 20, 97, 43, 83, 24, 160, 24, 85

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

FORMULA

Conjecture: Sum_{k=1..n} a(k) ~ n^2/2. - Vaclav Kotesovec, Jun 25 2024

EXAMPLE

a(6) = phi(2-1) + phi(3-1) + phi(6-1) = 1 + 1 + 4 = 6.

MATHEMATICA

f[n_] := Block[{k = Drop[Divisors[n], 1]}, Plus @@ EulerPhi[k - 1]]; Table[ f[n], {n, 75}] (* Robert G. Wilson v, Nov 12 2004 *)

PROG

(Magma)

f:= func< n | n eq 1 select 0 else EulerPhi(n-1) >;

A092843:= func< n | (&+[f(d): d in Divisors(n)]) >;

[A092843(n): n in [1..100]]; // G. C. Greubel, Jun 24 2024

(SageMath)

def A092843(n): return sum(euler_phi(k-1) for k in (1..n) if (k).divides(n))

[A092843(n) for n in range(1, 101)] # G. C. Greubel, Jun 24 2024

(PARI) a(n) = sumdiv(n, k, if (k>1, eulerphi(k-1))); \\ Michel Marcus, Jun 25 2024

CROSSREFS

Cf. A000010, A069949.

Sequence in context: A324890 A180240 A065228 * A078589 A077880 A198930

Adjacent sequences: A092840 A092841 A092842 * A092844 A092845 A092846

KEYWORD

nonn

AUTHOR

Leroy Quet, Nov 09 2004

EXTENSIONS

More terms from Robert G. Wilson v, Nov 12 2004

STATUS

approved