A349467 Numbers k such that A349410(k) = 1.

1, 2, 3, 5, 6, 7, 8, 9, 11, 13, 17, 19, 21, 23, 25, 28, 29, 31, 32, 33, 36, 37, 39, 40, 41, 43, 47, 48, 49, 51, 53, 57, 59, 61, 67, 69, 70, 71, 73, 75, 79, 81, 83, 87, 89, 90, 93, 96, 97, 98, 101, 103, 107, 109, 110, 111, 113, 120, 121, 123, 126, 127, 128, 129, 130

Offset: 1

Author

Tejo Vrush, Nov 18 2021

Keywords

• nonn

Comments

Does this sequence have density 1/3? This sequence has infinitely many terms because every prime number is a term.

The numbers of terms not exceeding 10^k for k = 1, 2, ... are 8, 50, 396, 3566, 33943, 332042, 3297317, 32983277, ... Apparently this sequence has an asymptotic density of about 0.33. - Amiram Eldar, Nov 18 2021

Crossrefs

Cf. A349410.

Programs

Mathematica

a[n_] := Module[{s = NestWhileList[n*DivisorSigma[0, #] &, 1, UnsameQ, All]}, Differences[Position[s, s[[-1]]]][[1, 1]]]; Select[Range[130], a[#] == 1 &] (* Amiram Eldar, Nov 18 2021 *)