A335397 Starts of runs of 3 consecutive numbers that have an equal number of unitary and nonunitary divisors (A048109).

22625, 28375, 40472, 48248, 49624, 58374, 59750, 102248, 103624, 107702, 112374, 129623, 136214, 136375, 164295, 187623, 190375, 197910, 199624, 211624, 221750, 246616, 264248, 275750, 280231, 298375, 300806, 312471, 346086, 349623, 352375, 356375, 372248, 382374

Offset

1,1

Links

Zak Seidov, Table of n, a(n) for n = 1..10000

Example

22625 is a term since 22625, 22626 and 22627 each have an equal number of unitary and nonunitary divisors. 22625 has 4 unitary divisors (1, 125, 181 and 22625) and 4 nonunitary divisors (5, 25, 905 and 4525), 22626 has 8 unitary divisors and 8 nonunitary divisors, and 22627 has 4 unitary divisors and 4 nonunitary divisors.

Mathematica

q[n_] := DivisorSigma[0, n] == 2^(PrimeNu[n] + 1); v = q /@ Range[3]; seq = {}; Do[v = Append[Drop[v, 1], q[k]]; If[And @@ v, AppendTo[seq, k - 2]], {k, 4, 2 * 10^5}]; seq

Crossrefs

Subsequence of A048109 and A335328.

Cf. A000005, A034444, A048105.

Sequence in context: A233856 A100420 A271444 * A251789 A105378 A279443

Adjacent sequences: A335394 A335395 A335396 * A335398 A335399 A335400

Keyword

nonn

Author

Zak Seidov and Amiram Eldar, Jun 06 2020

Status

approved