A051346 Numbers that can be written as k/d(k) in four or more ways, where d(k) = number of divisors of k.

11264, 14175, 28160, 44100, 46464, 51200, 64000, 82944, 95744, 96000, 107008, 109375, 109760, 116160, 129536, 151263, 162624, 163328, 174592, 192000, 208384, 224000, 230912, 239360, 242176, 242550, 246960, 264704, 267520, 281600, 286650, 290304, 298496, 302016

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Examples

			From _Jon E. Schoenfield_, Feb 18 2021: (Start)
11264 is a term because it can be written as k/d(k) in four ways:
k =  360448:  360448/d(360448)  =  360448/32 = 11264;
k =  585728:  585728/d(585728)  =  585728/52 = 11264;
k =  630784:  630784/d(630784)  =  630784/56 = 11264;
k = 1115136: 1115136/d(1115136) = 1115136/99 = 11264. (End)
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A051278, A051279, A051280, A217125, A217126, A217127.

Programs

Mathematica

(* Assuming 3*10^5 <= k <= 3*10^8 *) ClearAll[cnt]; cnt[] = 0; Do[ If[IntegerQ[n = k/DivisorSigma[0, k]], cnt[n]++; If[cnt[n] >= 4, Print[{n, k, cnt[n]}]]], {k, 3*10^5, 3*10^8}]; Select[Range[310000], cnt[#] >= 4 &] (* _Jean-François Alcover, Sep 28 2012 *)