A370650 Numbers whose number of infinitary divisors that are terms of A366242 is equal to the number of infinitary divisors that are terms of A366243.

1, 8, 12, 18, 20, 27, 28, 44, 45, 50, 52, 63, 64, 68, 75, 76, 92, 98, 99, 116, 117, 124, 125, 144, 147, 148, 153, 164, 171, 172, 175, 188, 207, 212, 216, 236, 242, 244, 245, 261, 268, 275, 279, 284, 292, 316, 324, 325, 332, 333, 338, 343, 356, 360, 363, 369, 387, 388, 400

Offset: 1

Author

Amiram Eldar, Feb 24 2024

Keywords

• nonn

Comments

Numbers k such that A366308(k) = A366309(k).

Numbers k such that A366246(k) = A366247(k) = A064547(k)/2.

If k is a term, then all the numbers with the same prime signature as k are terms. The least terms with each prime signature are listed in A370651.

p^A039004(k) is a term for all primes p and all k >= 1.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A037445, A039004, A064547, A366242, A366243, A366246, A366247, A366308, A366309.

A370651 is a subsequence.

Programs

Mathematica

s1[0] = 0; s1[n_] := s1[n] = s1[Floor[n/4]] + If[OddQ[Mod[n, 4]], 1, 0]; f1[p_, e_] := s1[e]; a1[1] = 0; a1[n_] := Plus  @@ f1 @@@ FactorInteger[n];
s2[0] = 0; s2[n_] := s2[n] = s2[Floor[n/4]] + If[Mod[n, 4] > 1, 1, 0]; f2[p_, e_] := s2[e]; a2[1] = 0; a2[n_] := Plus @@ f2 @@@ FactorInteger[n];
q[n_] := a1[n] == a2[n]; Select[Range[400], q]