A039004 -id:A039004 - cp's OEIS frontend

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

Amiram Eldar, Feb 24 2024

nonn

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.

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

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

A370651 is a subsequence.

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]

A370651 Terms of A370650 that are of least prime signature.

Original entry on oeis.org

1, 8, 12, 64, 144, 216, 360, 512, 768, 1152, 1260, 1728, 2880, 4096, 6144, 7200, 10800, 13824, 15360, 20736, 23040, 25200, 27000, 32768, 34560, 37800, 46656, 49152, 73728, 80640, 86400, 110592, 129600, 138600, 165888, 184320, 201600, 216000, 248832, 262144, 276480

Offset: 1

Amiram Eldar, Feb 24 2024

nonn

If k is a term, then all the numbers with the same prime signature as k are terms of A370650.

2^A039004(k) is a term for all k >= 1.

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

Intersection of A025487 and A370650.

Cf. A039004.

lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {, }][[;; , 2]]; Select[lps, q] (* using the function q[n] in A370650 *)

cp's OEIS Frontend

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.

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