A351910 Numbers k >= 1 such that A053818(k) divided by A000010(k) is an integer.

1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 30, 32, 34, 36, 40, 42, 44, 46, 48, 50, 54, 58, 60, 64, 66, 68, 72, 78, 80, 82, 84, 88, 90, 92, 94, 96, 100, 102, 106, 108, 110, 114, 116, 118, 120, 126, 128, 132, 136, 138, 142, 144, 150, 156, 160, 162, 164, 166, 168, 170

Offset

1,2

Comments

Also numbers k >= 1 such that the mean square of the Euler set of k is an integer.

Also numbers k >= 1 such that Sum_{i=1..k, gcd(k,i) = 1} i^2 is a multiple of phi(k), where phi is Euler's totient function.

Links

Table of n, a(n) for n=1..62.

Example

k = 40: A053818(40) = 8560, A000010(40) = 16, 8560/16 = 535 thus 40 is a term.

Mathematica

f[p_, e_] := -p^(1 - e); q[1] = True; q[n_] := IntegerQ[n * Times @@ f @@@ FactorInteger[n]/6 + n^2/3]; Select[Range[160], q] (* Amiram Eldar, Feb 25 2022, based on Brown's formula at A053818 *)

Prog

(PARI) isok(m) = denominator(sum(k=1, m, k^2*(gcd(m, k) == 1))/eulerphi(m)) == 1; \\ Michel Marcus, Feb 25 2022

Crossrefs

Cf. A000010, A053818.

Sequence in context: A002174 A002202 A049225 * A371177 A076450 A097379

Adjacent sequences: A351907 A351908 A351909 * A351911 A351912 A351913

Keyword

nonn

Author

Ctibor O. Zizka, Feb 25 2022

Status

approved