A382353 Numbers k > 0 such that A006218(k) / A018804(k) is an integer.

1, 2, 3, 4, 8, 10, 15, 43, 63, 6934, 316563, 2428132, 56264126

Offset: 1

Author

Ctibor O. Zizka, Mar 22 2025

Keywords

• nonn
• more

Comments

A006218(k) = A018804(k) for k = 1,2,3,4,8,10,15,63.

Examples

			k = 15: A006218(15)/A018804(15) = 45/45 = 1 is an integer, thus k = 15 is a term.
So far, the quotients are: 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 2, 2, 6.
		

Crossrefs

Cf. A006218, A018804.

Programs

Mathematica

f[p_, e_] := (e*(p-1)/p + 1)*p^e; pil[n_] := Times @@ f @@@ FactorInteger[n]; With[{max = 10^4}, Position[Accumulate[Array[DivisorSigma[0, #]&, max]] / Array[pil, max], ?IntegerQ] // Flatten] (* _Amiram Eldar, Mar 22 2025 *)

PARI

isok(m) = denominator(sum(k=1, m, m\k)/sumdiv(m, d, m*eulerphi(d)/d)) == 1; \\ Michel Marcus, Mar 22 2025

Extensions

a(11)-a(13) from Amiram Eldar, Mar 22 2025