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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.
2
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
1,2
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
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]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Feb 24 2024
STATUS
approved