A033859 Numbers k such that A033831(k) = A034444(k) where A034444(k) = number of unitary divisors of k.

8, 16, 24, 27, 36, 40, 54, 81, 88, 100, 104, 120, 125, 135, 136, 152, 168, 184, 189, 196, 225, 232, 248, 250, 264, 270, 272, 280, 296, 297, 312, 328, 343, 344, 351, 375, 376, 378, 408, 424, 440, 441, 456, 459, 472, 484, 488, 513, 520, 536, 568, 584, 594, 616

Offset: 1

Author

Naohiro Nomoto

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A033831, A034444.

Programs

Maple

with(numtheory): for n from 1 to 1200 do it := divisors(n): count := 0: for i from 1 to nops(it) do if it[i]>=3 and 1<=n/it[i] and n/it[i]<=(it[i]-2) then count := count+1 fi:od: if count=2^nops(ifactors(n)[2]) then printf(`%d,`,n) fi; od:

Mathematica

j[n_] := DivisorSum[n, 1&, # > 2 && n/# < #-1 &]; Select[Range[1000], j[#] == 2^PrimeNu[#] &] (* Amiram Eldar, Jun 11 2019 *)

Extensions

More terms from James Sellers, Jun 20 2000