A217126 -id:A217126 - cp's OEIS frontend

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

David W. Wilson

nonn

			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)

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

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

(* 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 *)

A217125 Numbers n such that n = k/d(k) has exactly 4 solutions, where d(k) = number of divisors of k.

Original entry on oeis.org

11264, 14175, 28160, 44100, 46464, 51200, 95744, 96000, 107008, 109375, 109760, 116160, 129536, 151263, 162624, 163328, 174592, 192000, 208384, 224000, 230912, 239360, 242176, 242550, 246960, 264704, 267520, 281600, 286650, 298496, 302016, 323840, 332288

Offset: 1

Donovan Johnson, Sep 27 2012

nonn

			k/d(k) = 11264 for exactly 4 k values: 360448, 585728, 630784 and 1115136.

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

Cf. A051278, A051279, A051280, A051346, A217126, A217127.

(* 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[350000], cnt[#] == 4 &] (* _Jean-François Alcover, Sep 28 2012 *)

A217127 Numbers n such that n = k/d(k) has exactly 6 solutions, where d(k) = number of divisors of k.

Original entry on oeis.org

82944, 456192, 705024, 787968, 953856, 1202688, 1285632, 1534464, 1700352, 1783296, 1949184, 2198016, 2446848, 2529792, 2778624, 2944512, 3027456, 3276288, 3345408, 3442176, 3691008, 3877632, 4022784, 4188672, 4271616, 4333824, 4437504, 4520448, 4686336

Offset: 1

Donovan Johnson, Sep 27 2012

nonn

			k/d(k) = 82944 for exactly 6 k values: 7962624, 12939264, 13271040, 13934592, 21565440 and 23224320.

Donovan Johnson, Table of n, a(n) for n = 1..300

Cf. A051278, A051279, A051280, A051346, A217125, A217126.

A051522 Least positive integer with exactly n representations as k/d(k), where d(k) = number of divisors of k.

Original entry on oeis.org

18, 4, 1, 3, 11264, 64000, 82944, 27599616

Offset: 0

David W. Wilson

27599616 is the only number < 4*10^7 with exactly 7 representations as k/d(k). - Donovan Johnson, Sep 29 2012

			Contribution from _Donovan Johnson_, Sep 29 2012: (Start)
a(1) = A051278(1) = 4. k/d(k) = 4 for exactly 1 k value: 36.
a(2) = A051279(1) = 1. k/d(k) = 1 for exactly 2 k values: 1 and 2.
a(3) = A051280(1) = 3. k/d(k) = 3 for exactly 3 k values: 9, 18 and 24.
a(4) = A217125(1) = 11264. k/d(k) = 11264 for exactly 4 k values: 360448, 585728, 630784 and 1115136.
a(5) = A217126(1) = 64000. k/d(k) = 64000 for exactly 5 k values: 4096000, 6656000, 7040000, 7168000 and 11520000.
a(6) = A217127(1) = 82944. k/d(k) = 82944 for exactly 6 k values: 7962624, 12939264, 13271040, 13934592, 21565440 and 23224320.
a(7) = 27599616. k/d(k) = 27599616 for exactly 7 k values: 10598252544, 17222160384, 17663754240, 18215746560, 18546941952, 28703600640 and 30911569920. (End)

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

a(4)-a(6) verified and a(7) added by Donovan Johnson, Sep 29 2012

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

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A217125 Numbers n such that n = k/d(k) has exactly 4 solutions, where d(k) = number of divisors of k.

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A217127 Numbers n such that n = k/d(k) has exactly 6 solutions, where d(k) = number of divisors of k.

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A051522 Least positive integer with exactly n representations as k/d(k), where d(k) = number of divisors of k.

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