Can I use this calculator offline?

Yes. Once the page has loaded, all calculations run locally in your browser, so results work even without an active internet connection.

Do you store or share the values I enter?

No. Your inputs are processed on your device and are not sent to our servers, stored on our side, or shared with third parties.

Does the page explain the formula behind the calculation?

Yes. Every calculator documents the formula it uses, shows the calculation step by step and includes at least one worked example with realistic numbers.

Amicable Pair Calculator

Free online amicable pair calculator. Enter your values and get instant results with the formula, step-by-step working, a worked example and FAQs — everything runs locally in your browser on Calcton, no signup required.

中文版：亲和数对在线计算器

N（列出所有 a < b ≤ N 的亲和数对，N ≤ 20000）

计算结果

≤ 20,000 内亲和数对8 对

全部数对220–284，1,184–1,210，2,620–2,924，5,020–5,564，6,232–6,368，10,744–10,856，12,285–14,595，17,296–18,416

判据s(a) = b 且 s(b) = a（s 为真因子和），且 a ≠ b

最经典的一对

220 = 1+2+4+5+10+11+20+22+44+55+110 之和的反向：s(220) = 284，s(284) = 220

毕达哥拉斯学派早已知道 (220, 284)；≤ 20000 内共 8 对，其中 (12285, 14595) 是唯一的奇数对。费马发现了 (17296, 18416)，欧拉一个人找到了约 60 对——但第二小的 (1184, 1210) 却迟至 1866 年才被 16 岁的帕加尼尼发现。

How to use the Amicable Pair Calculator

Fill in the inputs with your own numbers — every field shows what it expects.
The result updates instantly as you type; no "Calculate" click needed.
Read the result card for the main figure, the step-by-step formula, and practical notes.

Frequently asked questions

Is the Amicable Pair Calculator free?

Yes — all math calculators on Calcton are free, with no sign-up required. Your inputs are processed in your browser and never sent to a server.

Is there a Chinese version of this tool?

Yes. Use the Chinese version link above — it is the same calculator with the interface in Simplified Chinese.

References

Formulas and benchmarks used by this calculator follow these published sources.

KevinContent LeadCalcton Editorial Team · Last updated 2026-09-25

Kevin maintains Calcton's formula verification and content: every calculator cites the standard it implements, worked examples are recomputed programmatically, and health benchmarks follow WHO and international guidelines.

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