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

Author

Ctibor O. Zizka, Feb 25 2022

Keywords

• nonn

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.

Examples

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

Crossrefs

Cf. A000010, A053818.

Programs

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 *)

PARI

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