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IMO 2016 No 4 - Himpunan sukubanyak yang harum

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Suatu himpunan bilangan asli dikatakan $\it{harum}$ jika memiliki setidaknya dua anggota dan masing-masing anggota mempunyai faktor prima persekutuan dengan setidaknya satu anggota lainnya. Misalkan $P(n)=n^2+n+1$. Berapakah bilangan asli terkecil $b$ yang mungkin agar terdapat suatu bilangan bulat non-negatif $a$ sehingga himpunan $${P(a+1),P(a+2),\cdot,P(a+b)}$$ harum?

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