A382872 -id:A382872 - cp's OEIS frontend

A384020 Numbers k > 0 such that sigma(A018804(k)) = k*tau(A018804(k)) where sigma denotes the sum of divisors (A000203) and tau denotes the number of divisors (A000005).

1, 2, 3, 6, 7, 10, 14, 19, 21, 30, 31, 37, 38, 39, 42, 57, 62, 70, 74, 78, 79, 93, 97, 111, 114, 133, 139, 157, 158, 186, 190, 194, 199, 210, 211, 217, 222, 229, 237, 259, 266, 271, 273, 278, 291, 307, 310, 314, 331, 337, 367, 370, 379, 390, 398, 399, 410

Offset: 1

Ctibor O. Zizka, May 17 2025

nonn

Experimental result: the fraction of numbers k such that S(P(k)) > k*D(P(k)) tends to 0, S(P(k)) = k*D(P(k)) tends to 0, S(P(k)) < k*D(P(k)) tends to 1 with growing k where S(P(k)) denotes A000203(A018804(k)) and D(P(k)) denotes A000005(A018804(k)).

			For k = 6, a(6) = A000203(A018804(6)) = 6*A000005(A018804(6)).

Cf. A000005, A000203, A018804, A382872.

f[p_, e_] := (e*(p - 1)/p + 1)*p^e; pil[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[500], Divide @@ DivisorSigma[{1, 0}, pil[#]] == # &] (* Amiram Eldar, May 17 2025 *)

cp's OEIS Frontend

A384020 Numbers k > 0 such that sigma(A018804(k)) = k*tau(A018804(k)) where sigma denotes the sum of divisors (A000203) and tau denotes the number of divisors (A000005).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica