A387055 Numbers that are unitarily divisible by their number of divisors.

1, 2, 24, 36, 40, 56, 60, 84, 88, 104, 132, 136, 152, 156, 184, 204, 225, 228, 232, 248, 276, 296, 328, 344, 348, 372, 376, 424, 441, 444, 450, 472, 488, 492, 516, 536, 564, 568, 584, 600, 632, 636, 664, 708, 712, 732, 776, 804, 808, 824, 852, 856, 872, 876, 882, 904, 948, 996

Offset: 1

Author

Amiram Eldar, Aug 15 2025

Keywords

• nonn
• easy

Comments

Refactorable numbers (A033950) k whose number of divisors is a unitary divisor of k.

This sequence is infinite. For example, if p is an odd prime, then 8*p is a term.

Links

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

Crossrefs

Subsequence of A033950.

Cf. A000005, A023534, A048166, A077610.

Programs

Mathematica

q[k_] := Module[{d = DivisorSigma[0, k]}, Divisible[k, d] && CoprimeQ[d, k/d]]; Select[Range[1000], q]

PARI

isok(k) = {my(d = numdiv(k)); !(k % d) && gcd(d, k/d) == 1;}